Question

The 5th and 13^th terms of an AP are 5 and - 3 respectively. Find the 16th term of the same AP ?
1. - 7
2. 6
3. - 6
4. None of these

Answer 1

Correct Answer - Option 3 : - 6

CONCEPT:

Let us suppose a be the first term and d be the common difference of an AP. Then the nth term of an AP is given by: an = a + (n - 1) × d

CALCULATION:

Given: The 5th and 13th terms of an AP are 5 and - 3 respectively.

As we know that, if a is the first term and d is the common difference of an AP then an = a + (n - 1) × d

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

⇒ a₅ = a + 4d = 5 ------------(1)

⇒ a₁₃ = a + 12d = - 3--------(2)

By solving equation (1) and (2), we get

⇒ a = 9 and d = - 1

Here, we have to find the 16th term of the AP

⇒ a₁₆ = a + 15d = 9 - 15 = - 6

Hence, correct option is 3.