Question

the sum of third and seventh terms of a ap is 6 and their product is 8 find the sum of 16 terms​

Answer 1

Answer:

Step-by-step explanation:

a3=a+(3-1)d=a+2d

a7=a+(7-1)d=a+6d

given a3+a7=6

a3*a7=8--(2)

a+2d+a+6d=6

2a+8d=6

a+4d=3---(1)

solve (2)

(a+2d)(a+6d)=8

a^2+6ad+2ad+12d^2=8

a^2+8ad+12d^2=8

square (1) on both sides

a^2+16d^2+8ad=9

now solve the above two equations

4d^2=1

d=1/2

a+4(1/2)=3

a+2=3

a=1

now

s16=(16/2)(2+(15)*(1/2))

=8(2+15/2)

=8/2(19)

=4*19=76