**CBSE NCERT Solutions Chapter 5 Arithmetic Progressions Exercise 5.2 Question 16**

**16. Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.**

**Solution:**

Let first term of AP = a

Let common difference of AP = d

It is given that its 3rd term is equal to 16. It means , where is the 3rd term of AP.

**Using formula** , **to find** nth term of arithmetic progression, **we can say that**

**(1)**

It is also given that 7th term exceeds 5th term by12. Again using formula , which is used to find nth term of arithmetic progression, we can say that

And, **(1)**

According to the given condition, we can say that

Putting **(1) **in the above equation, we get

Putting value of d in equation , we get

Therefore first term = a = 4

And, common difference = d = 6

**Therefore, AP is 4, 10, 16, 22 ....**