Sequence and Series questions
1035 published questions with worked solutions.
- Let f(x) = 2^ x+2 +16 2^ 2x+1 +2^ x+4 +32 . Then the value of 8 (f ( 1 15 ) + f ( 2 15 ) + ... + f ( 59 15 ) ) is equal to
- In an arithmetic progression, if S_ 40 = 1030 and S_ 12 = 57, then S_ 30 - S_ 10 is equal to :
- If 7 = 5 + 1 7 (5+ ) + 1 7^2 (5+2 ) + 1 7^3 (5+3 ) + , then the value of is :
- If f(x) = 2^x 2^x+ 2 , x R, then _ k=1 ^ 81 f ( k 82 ) is equal to
- Let a_n be a sequence such that a_0 = 0, a_1 = 1 2 and 2a_ n+2 = 5a_ n+1 - 3a_n, n = 0, 1, 2, 3, .... Then _ k=1 ^ 100 a_k is...
- Let T_r be the r^ th term of an A.P. If for some m, T_m = 1 25 , T_ 25 = 1 20 and 20 _ r=1 ^ 25 T_r = 13, then 5m _ r=m ^ 2m T_r...
- The interior angles of a polygon with n sides, are in an A.P. with common difference 6°. If the largest interior angle of the...
- Consider an A.P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty terms lies...
- Let a_1, a_2, , a_ 2024 be an Arithmetic Progression such that a_1 + (a_5+a_ 10 +a_ 15 + +a_ 2020 )+a_ 2024 =2233. Then...
- The number of terms of an A.P. is even, the sum of all the odd terms is 24, the sum of all the even terms is 30 and the last term...
- If the sum of the first 10 terms of the series 4.1 1+4.1^4 + 4.2 1+4.2^4 + 4.3 1+4.3^4 + is m n , where gcd(m, n), then m + n is...
- Let a_1, a_2, a_3, be in an A.P. such that _ k=1 ^ 12 a_ 2k-1 = - 72 5 a_1, a_1 0. If _ k=1 ^ n a_k = 0, then n is :
- Three distinct numbers are selected randomly from the set 1, 2, 3, …, 40 . If the probability, that the selected numbers are in...
- The sum 1 + 3 + 11 + 25 + 45 + 71 + ..... upto 20 terms, is equal to
- Let a_1, a_2, a_3, be a G.P of increasing positive numbers. If a_3a_5 = 729 and a_2+a_4 = 111 4 , then 24(a_1+a_2+a_3) is equal to
- 1 + 3 + 5^2 + 7 + 9^2 + … upto 40 terms is equal to
- Let A = 1, 6, 11, 16, … and B 9, 16, 23, 30, … be the sets consisting of the first 2025 terms of two arithmetic progressions....
- If 1 1^4 + 1 2^4 + 1 3^4 +....... = ^4 90 , 1 1^4 + 1 3^4 + 1 5^4 +....... = 1 2^4 + 1 4^4 + 1 6^4 +....... = Then is equal to
- Consider two sets A and B, each containing three numbers in A.P. let the sum and the product of the elements of A be 36 and p...
- Let a_n be the nth term of an A.P. If S_n = a_1 + a_2 + a_3 + + a_n = 700, a_6 = 7 and S_7 = 7, then a_n is equal to :
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