Sequence and Series questions
1035 published questions with worked solutions.
- Five number are in A.P. , whose sum is 25 and product is 2520. If one of these five numbers is - 1 2 , then the greatest number...
- The sum _ k=1 ^ 20 (1+2+3+ +k) is ___________________.
- If the 10th term of an A.P is 1 20 and its 20th term is 1 10 , then the sum of its first 200 terms is :
- The sum, _ n=1 ^ 7 n(n+1)(2n+1) 4 is equal to ______.
- If the sum of first 11 terms of an A.P., a_1, a_2, a_3, ........ is 0 (a_1 0), then the sum of the A.P., a_1, a_3, a_5, ..., a_...
- Let S be the sum of the first 9 terms of the series: x+ka + x^2+(k+2)a + x^3+(k+4)a + x^4+(k+6)a + where a 0 and x 1. If S= x^ 10...
- A software company sets up m number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the...
- If |x| < 1, |y| < 1 and x ≠ y, then the sum to infinity of the following series (x+y)+(x^2+xy+y^2)+(x^3+x^2y+xy^2+y^3)+
- The sum of the first three terms of a G.P. is S and their product is 27. Then all such S lie in :
- If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common...
- In an increasing geometric progression of positive terms, the sum of the second and sixth terms is 70 3 and the product of the...
- If 1+(1-2^2 1)+(1-4^2 3)+(1-6^2 5)+ +(1-20^2 19)= -220 , then an ordered pair ( , ) is equal to :
- Let a_1, a_2, ….., a_n be a given A.P. whose common difference is an integer and S_n=a_1+a_2+ +a_n. If a_1=1, a_n=300 and 15 n...
- Let x and [x] denote the fractional part of x and the greatest integer x respectively of a real number x. If _0^n x dx, _0^n[x]dx...
- If 3^ 2 2 -1 , 14 and 3^ 4-2 are the first three terms of an A.P. for some , then sixth term of this A.P. is :
- If 2^ 10 +2^9 3^1+2^8 3^2+ +2 3^9+3^ 10 =S-2^ 11 , then S is equal to :
- If the sum of the first 20 terms of the series (7^ 1/2 )x+ (7^ 1/3 )x+ (7^ 1/4 )x+ is 460, then x is equal to :
- If the sum of the second, third and fourth terms of a positive term G.P. is 3 and the sum of its sixth, seventh and eighth terms...
- If f(x + y) = f(x) f(y) and _ x=1 ^ f(x)=2, x, y ∈ N, where N is the set of all natural numbers, then the value of f(4) f(2) is -
- The common difference of the A.P. b_1, b_2, ..., b_m is 2 more than the common difference of A.P. a_1, a_2, ..., a_n. If a_ 40 =...
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