Question

UA
UL,
(ii) The sum of the 4th and 8th term of an A.P. is 54 and their product is 665. Find the sum of the first 30 term
of the A.P. (The terms of the AP are in ascending order)​

Answer 1

Answer:

1920

Step-by-step explanation:

A4+A8=54

a+3d+a+7d=54

2a+10d=54

a+5d=27

a=27-5d ____eq.1

A4×A8=665

(a+3d)(a+7d) = 665

(27-5d+3d)(27-5d+7d)=665

(27-2d)(27+2d)=665

729+54d-54d-4d^2=665

-4d^2=665-729

-4d^2=-64

d^2=16

d=4

put the value of d in eq.1

a=27-5×4

a=26-20

a=6

a=6,d=4,n=30

Sn=n/2[2a+(n-1)d]

S30=30/2[2×6+(30-1)×4]

S30=30/2[12+116]

S30=30/2×128

S30=30×64

S30=1920