from a handpicked tutor in LIVE 1-to-1 classes

# 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,…

**☛ Related Questions:**

- Find the 20th term from the last term of the A.P. 3, 8, 13,..., 253.
- The sum of the 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the A.P.
- Subba Rao started work in 1995 at an annual salary of Rs 5000 and received an increment of Rs 200 each year.
- Ramkali saved Rs 5 in the first week of a year and then increased her weekly saving by Rs 1.75. If in the nth week, her weekly savings become Rs 20.75, find n.

visual curriculum