List of top Mathematics Questions on Sequence and series asked in BITSAT

The sum of the infinite geometric series $ S = \frac{a}{1-r} $ is 24, and the sum of the first three terms is 21. Find $ a $ and $ r $.
For all \( n \in \mathbb{N} \), the sum of \( \frac{n^5}{5} + \frac{n^3}{3} + \frac{7n}{15} \) is:
If the sum of an infinite GP \( a, ar, ar^2, ar^3, \dots \) is 15 and the sum of the squares of each term is 150, then the sum of the series \( ar^2, a r^4, ar^6, \dots \) is:
$2^{1/4}. 2^{2/8}. 2^{3/16}. 2^{4/32}......\infty$ is equal to-
The value of $\frac{3}{4} + \frac{15}{16} +\frac{63}{64} +..... $ upto n terms is
Let $T(k)$ be the statement $1 + 3 + 5 + ... + (2k - 1)= k^2 +10$ Which of the following is correct?