Question

In an A.P. if the first term is 4 and 9^th term is 20 then 15^th term is

• A. 16
• B. 32
• C. 18
• D. 36

Answer 1

The Correct Option is B

To solve the problem, we need to find the $15^{\text{th}}$ term of an arithmetic progression (A.P.) given:

• First term $a = 4$
• $9^{\text{th}}$ term $T_9 = 20$

1. General Formula for the $n^{\text{th}}$ Term:
The general term of an A.P. is given by:

$ T_n = a + (n - 1)d $
where $a$ is the first term and $d$ is the common difference.

2. Use the Given $9^{\text{th}}$ Term:
We know $T_9 = 20$:

$ a + 8d = 20 $
Substitute $a = 4$:
$ 4 + 8d = 20 $
$ 8d = 16 \Rightarrow d = 2 $

3. Finding the $15^{\text{th}}$ Term:
Use the formula again:
$ T_{15} = a + 14d = 4 + 14 \times 2 = 4 + 28 = 32 $

Final Answer:
The $15^{\text{th}}$ term is $ {32} $.