In arithmetic progression (A.P.), the first term is 7 and the 6th term is 22. The sum of the first 10 terms of A.P. is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 205
In an A.P. with first term \(a\) and common difference \(d\), the \(n\)th term is \(a+(n-1)d\) and the sum of the first \(n\) terms is \(\frac{n}{2}\left[2a+(n-1)d\right]\).
The common difference (the 6th term is 22):
\(7+5d=22\)
\(5d=15\), so \(d=3\)
The sum of the first 10 terms:
\(\displaystyle S_{10}=\frac{10}{2}\left[2\times7+9\times3\right]=5\times41=205\)