Sequence and Series questions
1035 published questions with worked solutions.
- In a increasing geometric series, the sum of the second and the sixth term is 25 2 and the product of the third and fifth term is...
- The sum of the infinite series 1+ 2 3 + 7 3^2 + 12 3^3 + 17 3^4 + 22 3^5 + equal to
- If a_ i _ i=1 ^ n , where n is an even integer, is an arithmetic progression with common difference 1, and _ i=1 ^na_i = 192, _...
- Let a_ 1 = b_ 1 = 1, a_ n = a_ n-1 + 2 and b_ n = a_ n + b_ n-1 for every natural number n 2. Then _ n=1 ^ 15 a_ n b_ n is equal...
- The sum 1 + 2·3 + 3 3^ 2 + …. + 10 3^ 9 is equal to-
- Let f : ℕ ℝ be a function such that f(x + y) = 2f(x)f(y) for natural numbers x and y. If f(1) = 2, then the value of for which _...
- If 1/(2 3^ 10 ) + 1/(2^ 2 3^ 9 ) + … + 1/(2^ 10 3) = K/(2^ 10 3^ 10 ), then the remainder when K is divided by 6 is -
- If _ k=1 ^ 10 k/(k^ 4 + k^ 2 + 1) = m/n, where m and n are co-prime, then m + n is equal to _____
- Different A.P.'s are constructed with the first term 100, the last term 199, and integral common differences. The sum of the...
- Consider two G.P.s 2, 2^ 2 , 2^ 3 , .... and 4, 4^ 2 , 4^ 3 , ... of 60 and n terms respectively. If the geometric mean of all...
- The series of positive multiples of 3 is divided into sets: 3 , 6, 9, 12 , 15, 18, 21, 24, 27 , _____ Then the sum of the...
- If A = _ n=1 ^ 1 (3+(-1)^n)^n and B = _ n=1 ^ (-1)^n (3+(-1)^n)^n , then A/B is equal to :
- If a_ 1 (> 0), a_ 2 , a_ 3 , a_ 4 , a_ 5 are in a G.P., a_ 2 + a_ 4 = 2a_ 3 + 1 and 3a_ 2 + a_ 3 = 2a_ 4 , then a_ 2 + a_ 4 + 2a_...
- Let A = _ i=1 ^ 10 _ j=1 ^ 10 i, j and B = _ i=1 ^ 10 _ j=1 ^ 10 i, j . Then A + B is equal to _____.
- Let a_1, a_2, a_3, … be an A.P. If a_1+a_2+ +a_ 10 a_1+a_2+ +a_p = 100 p^2 , p 10, then a_ 11 a_ 10 is equal to :
- If S = 7 5 + 9 5^2 + 13 5^3 + 19 5^4 + , then 160 S is equal to_____.
- The sum of the common terms of the following three arithmetic progressions. 3, 7, 11, 15, …, 399, 2, 5, 8, 11, …, 359 and 2, 7,...
- The sum to 10 terms of the series 1 1+1^2+1^4 + 2 1+2^2+2^4 + 3 1+3^2+3^4 + is
- Let a_1 = 8, a_2, a_3, …a_n be an A.P. If the sum of its first four terms is 50 and the sum of its last four terms is 170, then...
- If (20)^ 19 +2(21)(20)^ 18 +3(21)^2(20)^ 17 + +20(21)^ 19 =k(20)^ 19 , then k is equal to __________.
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