The 7th and 9th terms of an arithmetic progression are 10 and 11, respectively. Find the 15th term.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 14
In an arithmetic progression each term is the previous one plus a fixed common difference \(d\), so \(a_n=a+(n-1)d\). Two given terms fix \(d\), and \(d\) then leads to any other term.
From the 7th term to the 9th term is 2 steps: \(2d=11-10=1\), so \(d=\frac{1}{2}\)
From the 9th term to the 15th term is 6 steps: \(a_{15}=a_9+6d\)
\(\displaystyle a_{15}=11+6\times\frac{1}{2}=11+3=14\)