# Sequences and Series

**Question**

A. Solve the following questions related to a series.

- In an arithmetric progression, the 10th term is 21 while the 12nd term is 25. Find the common difference (d) and also the first two terms of the series.
- If the sum of the nth terms in an arithmetic progression is Sn = 3n + n
^{2}, find the 5th term of the series.

*Guide:*

*The formula to find the nth term in an arithmetic progression is: a*_{n}= a + (n-1)d*The formula to find the sum of the nth terms in an arithmetic progression is Sn = n/2(2a + (n-1)d)*

**Answer**

- d = 2, a1 = 3, a2 = 5
- a5 = 12

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