# Determine the A.P. whose third term is 16 and the 7th term exceeds the 5th term by 12

**Solution:**

a_{n} = a + (n - 1)d is the general term of AP. Where a_{n }is the nth term, a is the first term, d is a common difference and n is the number of terms.

Let a be the first term and d the common difference.

According to the question, a_{3} = 16 and a_{7} - a_{5} = 12

a + (3 - 1)d = 16

a + 2d = 16 ... Equation(1)

Using a_{7} - a_{5} = 12

[a + (7 - 1) d] - [a + (5 - 1) d] = 12

[a + 6d] - [a + 4d] = 12

2d = 12

d = 6

By substituting this in Equation (1), we obtain

a + 2 × 6 = 16

a + 12 = 16

a = 4

Therefore, A.P. will be 4, 4 + 6, 4 + 2 × 6, 4 + 3 × 6, ...

Hence, the sequence will be 4, 10, 16, 22, ...

Answer: The sequence will be 4, 10, 16, 22, ...

**Video Solution:**

## Determine the A.P. whose third term is 16 and the 7th term exceeds the 5th term by 12

### NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2 Question 16 - Chapter 5 Exercise 5.2 Question 16:

Determine the A.P. whose third term is 16 and the 7th term exceeds the 5th term by 12

The AP whose third term is 16 and the 7th term exceeds the 5th term by 12 is 4, 10, 16, 22,…