# Sequences and Series

**Question**

A. Solve the following questions related to a series.

- If the sum of the nth terms in an arithmetic progression is Sn = 3n + n
^{2}, find the 5th term of the 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.

*Guide:*

*The formula to find the sum of the nth terms in an arithmetic progression is Sn = n/2(2a + (n-1)d)**The formula to find the nth term in an arithmetic progression is: a*_{n}= a + (n-1)d*When taking H2 mathematics class, you will learn about things like concept of sequence and series for finite cases and infinite cases, sum and difference of two series, use of sigma notation and other interesting features of sequence and series.*

**Answer**

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

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