Sequence and Series questions
1035 published questions with worked solutions.
- If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the sum of its eighth, tenth and twelfth...
- Let A= 1,a_1,a_2, ,a_ 18 ,77 be a set of integers with 1<a_1<a_2< <a_ 18 <77. Let the set A+A= x+y:x,y A contain exactly 39...
- If a function F is such that F(0)=2, F(1)=3 and F(n+2)=2F(n)-F(n+1) for n 0, then F(5) is equal to
- If f(x)=2^x, then f(0),f(1),f(2), are in
- If 8 , x, 3 8 are in A.P. and 8 , y, 4 are in A.P., then find y x .
- If , 2 +2, 3 +3 are in GP, then the value of 7-5 9-4 ^2 -1 is
- If ( - ), and ( + ) are in HP, then 2 is equal to
- Let , be any two positive values of x for which 2 x, | x| and 1-3 ^2x are in GP. The minimum value of | - | is
- Statement 1: If x+ x= y+ 1y , x [0, ], then x= 4 , y=1. Statement 2: AM GM.
- In a right-angled triangle, if the sides are in AP, then their ratio is
- Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the...
- If (10)^9 + 2(11)^1(10)^8 + 3(11)^2(10)^7 + + 10(11)^9 = k(10)^9, then k is equal to:
- If the 2^ nd , 5^ th and 9^ th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is
- If the sum of the first ten terms of the series (1 3 5 )^2 + (2 2 5 )^2 + (3 1 5 )^2 + 4^2 + (4 4 5 )^2 + , is 16 5 m, then m is...
- Let a_1, a_2, a_3, , a_ 49 be in A.P. such that _ k=0 ^ 12 a_ 4k+1 = 416 and a_9 + a_ 43 = 66. If a_1^2 + a_2^2 + + a_ 17 ^2 =...
- Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series 1^2 + 2 2^2 + 3^2 + 2 4^2 + 5^2 + 2...
- Let 1 x_1 , 1 x_2 , 1 x_3 , , (x_i 0 for i = 1, 2, , n) be in A.P. such that x_1 = 4 and x_ 21 = 20. If n is the least positive...
- The sum of the first 20 terms of the series 1 + 3 2 + 7 4 + 15 8 + 31 16 + is ?
- The sum _ k=1 ^ 20 k , 1 2^k is equal to:
- Let _ k=1 ^ 10 f(a + k) = 16(2^ 10 - 1), where the function f satisfies f(x + y) = f(x)f(y) for all natural numbers x, y and f(1)...
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