Sequence and Series questions
1035 published questions with worked solutions.
- If a, x, b are in AP, a, y, b are in GP and a, z, b are in HP such that x = 9z and a > 0, b > 0 then
- If three numbers are in HP then the numbers obtained by subtracting half of the middle number from each of them are in
- a, b, c, d, e are five numbers in which the first three are in AP and the last three are in HP. If the three numbers in the...
- If S_r denotes the sum of the first r terms of an AP then S_ 3r -S_ r-1 S_ 2r -S_ 2r-1 is equal to
- S_r denotes the sum of the first r terms of a GP. Then S_n, S_ 2n -S_n, S_ 3n -S_ 2n are in
- If the sum of the series 1+ 2x+ 4 x^2 + 8 x^3 + to is a finite number then
- Let S_n denote the sum of the first n terms of an AP. If S_ 2n =3S_n then S_ 3n :S_n is equal to
- In a GP of even number of terms, the sum of all terms is 5 times the sum of the odd terms. The common ratio of the GP is
- In an AP, S_p=q, S_q=p and S_r denotes the sum of the first r terms. Then S_ p+q is equal to
- If a, b, c are in AP then a+ 1 bc , b+ 1 ca , c+ 1 ab are in
- The AM of two given positive numbers is 2. If the larger number is increased by 1, the GM of the numbers becomes equal to the AM...
- Let a, b be two positive numbers, where a>b and 4 GM =5 HM for the numbers. Then a is
- Let a_1=0 and a_1, a_2, a_3, , a_n be real numbers such that |a_i|=|a_ i-1 +1| for all i then the AM of the numbers a_1, a_2,...
- If the first and the (2n-1)th terms of an AP, a GP and an HP are equal and their nth terms are a, b and c respectively then
- a^n+b^n a^ n-1 +b^ n-1 is the HM between a and b if n is
- Let x be the AM and y, z be two GMs between two positive numbers. Then y^3+z^3 xyz is equal to
- If a, b, c are in AP, and p, p' are the AM and GM respectively between a and b, while q, q' are the AM and GM respectively...
- If a_n>1 for all n N then _ a_2 a_1+ _ a_3 a_2+ + _ a_n a_ n-1 + _ a_1 a_n has the minimum value
- The product of n positive numbers is 1. Their sum is
- If x, y, z are three real numbers of the same sign then the value of xy+ yz+ zx lies in the interval
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