List of top Mathematics Questions on sequences asked in KEAM

The 25th term of 9, 3, 1, \( \frac{1}{3} \), \( \frac{1}{9} \), ... is:

The general term of a sequence is \( t_n = \frac{n(n+6)}{n+4}, \, n = 1,2,3,\ldots \). If \( t_n = 5 \), then the value of \( n \) is

Let \( f:\mathbb{N}\to\mathbb{N} \) be such that \( f(1)=2 \) and \( f(x+y)=f(x)f(y) \). If \( \sum_{k=1}^{n} f(a+k)=16(2^n-1) \), then \( a \) is

Let \( f:\mathbb{N}\to\mathbb{N} \) be such that \( f(1)=2 \) and \( f(x+y)=f(x)f(y) \). If \( \sum_{k=1}^{n} f(a+k)=16(2^n-1) \), then \( a \) is

A function \(f\) satisfies the relation \( f(n^2) = f(n) + 6 \) for \(n \ge 2\) and \( f(2) = 8 \). Then the value of \( f(256) \) is

If \( a, b, c \) are in A.P. and their squares in same order form a G.P., then \( (a+c)^4 = \)

If \( f(1)=1 \), \( f(2n)=f(n) \) and \( f(2n+1)=(f(n))^2 - 2 \) for \( n=1,2,3,\ldots \), then the value of \( f(1)+f(2)+\cdots+f(25) \) is equal to