If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first 20 terms is equal to

Question

TestHub · Accepted Answer

​ a = 3 S 4 ​ = 5 1 ​ ( S 8 ​ − S 4 ​ ) ⇒ 5 S 4 ​ = S 8 ​ − S 4 ​ ⇒ 6 S 4 ​ = S 8 ​ ⇒ 6 ⋅ 2 4 ​ [ 2 × 3 + ( 4 − 1 ) × d ] = 2 8 ​ [ 2 × 3 + ( 8 − 1 ) d ] ⇒ 12 ( 6 + 3 d ) = 4 ( 6 + 7 d ) ⇒ 18 + 9 d = 6 + 7 d ⇒ d = − 6 S 20 ​ = 2 20 ​ [ 2 × 3 + ( 20 − 1 ) ( − 6 )] = 10 [ 6 − 114 ] = − 1080 ​

Mathematics - Sequence & Series Question with Solution | TestHub

Options:

Doubts & Discussion