Which term of the A.P. 7, 13, 19, 26, . . . . is 97?

The correct answer is Option (2) → 16^th

In an arithmetic progression (A.P.) each term is the previous one plus a fixed common difference \(d\), so the \(n\)th term is \(a_{n}=a+(n-1)d\).

• First term \(a=7\), common difference \(d=13-7=6\)

• \(7+(n-1)\times6=97\)

• \((n-1)\times6=90\), so \(n-1=15\)

• \(n=16\): 97 is the 16th term

Note: It seems that there is a mistake in the original NTA paper, which prints the fourth term as 26 when it should read 25. The first three terms 7, 13, 19 go up by 6 each time, so the fourth term is \(19+6=25\), and the answer is unaffected.