# Determine the AP whose third term is 16 and the 7^{th} term exceeds the 5^{th} term by 12

**Solution:**

aₙ = a + (n - 1)d is the n^{th} term of an AP, where aₙ_{ }is the n^{th} 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, a₃ = 16 and a₇ - a₅ = 12

a + (3 - 1)d = 16

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

Using a₇ - a₅ = 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, ...

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 5

**Video Solution:**

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

NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2 Question 16

**Summary:**

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

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