If the sum of first 14 terms of an AP is 1050 and its first term is 10, then its 20th term is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 200
The sum of the first \(n\) terms of an AP is \(S_n=\displaystyle\frac{n}{2}\left[2a+(n-1)d\right]\), and the \(n\)th term is \(a_n=a+(n-1)d\). The given sum fixes the common difference \(d\).
Sum of the first 14 terms: \(S_{14}=\displaystyle\frac{14}{2}\left[2\times10+13d\right]=7(20+13d)=1050\)
Common difference: \(20+13d=150\), so \(d=10\)
The 20th term: \(a_{20}=10+19\times10=200\)