Sequences and Series

What is the 10th term of the arithmetic progression (AP) 3, 7, 11, 15, ...?

Find the sum of the first 20 natural numbers.

If the 5th term of a geometric progression (GP) is 48 and the 8th term is 384, what is the common ratio?

The sum of the first n terms of an AP is given by S_n = 3n^2 + 5n. What is the first term?

Find the sum of the infinite geometric series 5 + (5/3) + (5/9) + (5/27) + ...

If the sum of first n terms of a series is S_n = 2^n - 1, what is the nth term T_n?

The 12th term of an AP is 32 and the 5th term is 17. Find the first term.

Find the sum of all two-digit numbers divisible by 7.

If the sum of the first n terms of a GP is 364 and the sum of first 2n terms is 4095, find the common ratio (r) if a = 1.

The sum of the first n terms of an AP is 5n^2 + 3n. Find the 10th term.