If the 5th and 9th terms of an arithmetic progression are 7 and 13, respectively, then the 15th term is:

22

The correct answer is Option (1) → 22

Step 1: Recall formula for the n-th term of an AP

$a_n = a_1 + (n-1)d$

where $a_1$​ = first term, d = common difference.

Step 2: Write equations for given terms

• 5th term: $a_5 = a_1 + 4d = 7$
• 9th term: $a_9 = a_1 + 8d = 13$

Step 3: Solve for d

$a_9 - a_5 = (a_1 + 8d) - (a_1 + 4d) = 4d = 13 - 7 = 6$

$d = \frac{6}{4} = 1.5$

Step 4: Solve for $a_1$​

$a_5 = a_1 + 4d = 7 \Rightarrow a_1 + 4(1.5) = 7$

$a_1 + 6 = 7 \Rightarrow a_1 = 1$

Step 5: Find 15th term

$a_{15} = a_1 + 14d = 1 + 14(1.5) = 1 + 21 = 22$