If the 5th and 9th terms of an arithmetic progression are 7 and 13, respectively, then the 15th term is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 22
In an arithmetic progression the \(n\)th term is \(a+(n-1)d\), so two terms 4 places apart differ by \(4d\); this gives \(d\) at once.
\(a+4d=7\) (1)
\(a+8d=13\) (2)
Subtracting (1) from (2), \(a\) cancels: \(4d=6\), so \(d=1.5\)
The 15th term is 6 places after the 9th: \(13+6\times1.5=13+9=22\)