Progression and Series — practice questions

82 curated practice questions from Progression and Series (Mathematics JEE Advanced, NTA Exams) — 54 hard, 28 medium. Every question includes the final answer free; step-by-step worked solutions with a free account.

• Four distinct integers a, b, c, d are in A.P. If a 2 + b 2 + c 2 = d, then a + b + c + d =
• Assertion : If all terms of a series with positive terms are smaller than 10 –5 , then the sum of the series upto…
• If x > 1, y > 1, z > 1 are in G.P. then 1/1+ln x , 1/1+ln y , 1/1+ln z are in
• If the first and the (2n – 1) th term of an AP, GP and HP are equal and their nth terms are a, b and c respectively…
• The sum of the first 10 terms of 3 2 + 5 4 + 9 8 + 17 16 + is
• Let x be the arithmetic mean and y, z be the two geometric means between any two positive number. Then value of is
• If a , b and c are distinct positive numbers, then the expression ( b + c – a ) ( c + a – b ) ( a + b – c ) – abc is
• If p, q, r are in A.P., then pth, qth and rth terms of any G.P. are in
• The harmonic mean of roots of the equation is
• A series whose nth term is n x + y , the sum of r terms will be
• If the sum of the first 2 n terms of the A.P. 2, 5, 8.......is equal to the sum of the first n terms of the A.P. 57…
• If x = 111 ... 1 (20 digits), y = 333...3 (10 digits) and z = 222...2 (10 digits), then x-y^ 2 z =
• If α, β be roots of x 2 – 3x + a = 0 and γ, δ are the roots of x 2 – 12x + b = 0 and α, β, γ, δ (in order) form an…
• Assertion : If three positive numbers in G.P. represent sides of a triangle, then the common ratio of the G.P. must lie…
• Let A 1 , G 1 and H 1 denote the arithmetic, geometric and harmonic means respectively of two distinct positive…
• Six arithmetic means are inserted between 1 and 9/2, the 4 th arithmetic mean is
• The product of n positive numbers is unity. Then their sum is
• If x _ 1 ^ 2 + x _ 2 ^ 2 + x _ 3 ^ 2 + .+ x _ B ^ 2 = n and 1 x _ 1 ^ 2 x _ 2 ^ 2 x _ B ^ 2 = A then
• If a, b, c are three unequal numbers such that a, b, c are in A.P. and b – a, c – b, a are in G.P., then a : b : c =
• If a, 4, b are in AP; a, 2, b are in G.P., then a, 1, b are in
• If the sum of first n terms of an A.P. is cn 2 , then the sum of squares of these n terms is
• The value of 9 1/3 . 9 1/9 . 9 1/27 ...... will be
• If a, b, c are in H.P., then the value of b + a ~b - a + b + c ~b - c is
• Let the positive numbers a , b , c , d be in A.P. then abc , abd , acd , bcd , are
• If the sum of m consecutive odd integers is m 4 , then the first integer is
• The sum of the n terms of the series 1 + (1 + 3) + (1 + 3 + 5) ....
• Sum of the first n terms of the series 1 2 + 3 4 + 7 8 + 15 16 + . is equal to
• If a , b , c , d and p are distinct real numbers such that ( a 2 + b 2 + c 2 ) p 2 – 2 ( ab + bc + cd ) p + ( b 2 + c 2…
• Statement 1 : The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) + ... + (361 + 380 + 400) is 8000 …
• The sum of three consecutive terms in G.P. is 14. If 1 is added to the first and the second term and 1 subtracted from…
• Let _ r =1 ^ n r ^ 4 =f( n ) then _ r =1 ^ n (2 r -1)^ 4 is equal to
• If 5x – y, 2x + y, x + 2y are in A.P. and (x–1) 2 , (xy + 1), (y+1) 2 are in G.P., x ≠ 0, then x + y =
• Let S_ n = _ k=1 ^ 4 n (-1)^ k(k+1) 2 k^ 2 Then S n can take value(s).
• Let S 1 , S 2 , ..... be squares such that for each n ≥ 1, the length of a side of S n , equals the length of a…
• The harmonic mean between two numbers is 14 2 5 and the geometric mean is 24. The greatest number between them is :
• Given p A.P.’s, each of which consists of n terms. If their first terms are 1, 2, 3, ...., p and common differences are…
• If nth term of a series is 1 (n+1)(n+3) , then sum of infinite terms of the series
• Let a 1 , a 2 , ..., a 10 be in A.P. and h 1 , h 2 , ..., h 10 be in H.P. If a 1 = h 1 = 2 and a 10 = h 10 = 3, then a…
• The third term of geometric progression is 4, the product of the first 5 terms is,
• The sum of the series 1 3 + 3 3 + 5 3 + ... to 20 terms is
• Consider the sequence 1, 2, 2, 3, 3, 3 ... where n occurs n times. The number that occurs as 2007 th term is
• Let a 1 , a 2 , a 3 , .... be in harmonic progression with a 1 = 5 and a 20 = 25 . The least positive integer n for…
• If the sum of n terms of G.P. is S, product is P and sum of their inverses is R, then P 2 =
• If the first two terms of a progression are log 2 256 and log 3 81 respectively, then which of the following statements…
• In a G.P. if the (m + n) th term be p and (m – n) th term be q then the m th term is
• If the third term of a G.P. is 4, then the product of its first 5 terms is
• If the first and the (2 n – 1) th term of an A.P., a G.P. and a H.P. are equal and their n th terms are a , b and c…
• If the sum of the 10 terms of an A.P. is 4 times to the sum of its 5 terms, then the ratio of first term and common…
• If a, b, c are 3 positive numbers in A.P. and a 2 , b 2 , c 2 are in H.P., then
• The first and last term of an A.P. are a and l respectively. If s be the sum of all terms of the A.P., then common…
• If ln ( a + c ), ln ( c – a ), ln ( a – 2 b + c ) are in A.P., then
• Suppose a , b , c are in A.P. and a 2 , b 2 , c 2 are in G.P. If a b c and a + b + c = , then the value of a is
• A G.P. consist of even number of terms. If the sum of the terms occupying the odd places is S 1 and that of the terms…
• The largest positive term of the H.P., whose first two terms are 2 5 and 12 23 is
• An infinite G.P. has first term ‘ x ’ and sum ‘5’, then
• 1 2 – 2 2 + 3 2 – 4 2 + ... to 21 terms =
• If the sum to n terms of a series be 5n 2 + 2n, then second term is
• For 0 and z= _ n=0 ^ ^ 2 n ^ 2 n , then
• If a, b and c are positive real numbers then a b + b c + c a is greater than or equal to
• Let a 1 , a 2 , a 3 , .... be an arithmetic progression with a 1 = 7 and common difference 8 . Let T 1 , T 2 , T 3 …
• Column I consist of progression which roots of equation a x^ 3 +b x^ 2 +c x+d=0 form and column II consist of relation…
• The sum of an infinite G.P. series is 3. A series which is formed by squares of its terms have the sum also 3. First…
• If one G.M., g and two A.M.’s p and q are inserted between two number a and b, then (2 p-q)(p-2 q) g^ 2 =
• If x 1 , x 2 , x 3 as well as y 1 , y 2 , y 3 are in G.P. with the same common ratio, then the points ( x 1 , y 1 ), (…
• If a, b, c are in A.P., then a b c , 1 c , 2 b are in
• If a, b, c are in H.P., then which one of the following is true
• Assertion : There exists an A.P. whose three terms are 2 , 3 , 5 . Reason : There exists distinct real numbers p, q, r…
• For a positive integer n . Let a(n)=1+ 1 2 + 1 3 + .+ 1 2^ n -1 then
• The sum of n terms of the following series 1 + (1 + x) + (1 + x + x 2 ) + . . . will be
• Column I consist of some terms where a,b,c are in HP and Column II consist of name of corresponding progression formed…
• Let b i > 1 for i = 1, 2, ..., 101. Suppose log e b 1 , log e b 2 , ...., log e b 101 are in arithmetic progression…
• If l n (x + z) + l n (x – 2y + z) = 2 l n (x – z), then x, y, z are in
• If a 1 , a 2 , ........... , a n are positive real numbers whose product is a fixed number c , then the minimum value…
• If a , b , c are in G.P then the equations ax 2 + 2 bx + c = 0, dx 2 + 2 ex + f = 0 have a common root if d a , e b , f…
• If a, b and c are positive real numbers, then the least value of (a + b + c) ( 1 a + 1 b + 1 c ) is
• If S_ n = 1 2 n - 1 n+1 + 1 2(n+2) then _ n=1 ^ 15 S_ n = 135 k , then the numerical quantity k must be
• Assertion : The sum of an infinite A.G.P. a + (a + d) x + (a + 2d) x 2 + (a + 3d) x 3 +.........., where | x | Reason …
• If a 1 , a 2 , a 3 , . . ., a n are in A.P. where a i > 0 then 1 a_ 1 + a_ 2 + 1 a_ 2 + a_ 3 + + 1 a_ n-1 + a_ n =
• The least value of n for which the sum 1 + 3 + 3 2 + .... to n terms is greater than 7000 is
• Let T r be the r th term of an A.P. for r = 1, 2, 3, ................. If for some positive integers m , n we have T m…
• The sum of series 1.3 2 + 2.5 2 + 3.7 2 + . . . upto 20 terms is
• Consider an infinite geometric series with first term a and common ratio r . If its sum is 4 and the second term is…

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