The sum of the first term and the sixth term of an A.P. is 28 and the product of the second term and the fourth term is 160. What is the sum of the first six terms of the A.P.?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 84
The sum of the first \(n\) terms of an A.P. is \(S_n=\frac{n}{2}(\text{first term}+\text{last term})\). For six terms the last term is the sixth, and the question gives first term \(+\) sixth term \(=28\) directly.
\(S_6=\frac{6}{2}(a_1+a_6)\)
\(S_6=3\times28=\) 84
The product of the second and fourth terms is not needed for this sum.
Tip: Whenever a question gives the sum of the first and last terms (or of any two terms equally far from the ends), the sum of the A.P. follows at once from \(\frac{n}{2}(a_1+a_n)\), without finding \(a\) and \(d\).