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 2
Let the five terms of the A.P. :-
a−2d, a−d, a, a+d, a+2d
Sum of the first and fifth terms is (a−2d)+(a+2d)=2a
2a= 28
a=14
Product of second and fourth terms is (a−d)(a+d)
= a² - d²
ATQ,
a² - d² = 160
196 - d² = 160
d² = 9
Is is an ascending AP . So d must be positive .
So, d = 3
Sum of n terms in an A.P is =n/2(2a+(n−1)d)
Here the first term is a−2d
Sum of 6 terms=
S=6/2 ( 2( 14 - 6 ) + (6 - 1 ) )3
= 3 ( 16 + (6 - 1 ) )3
=189
The correct answer is Option (2) → 189