Question

the sum of third and seventh term of an ap is 6 and their product is 8 find sum of first 20terms

Answer 1

t3= a+2d
t7= a+6d
t3+ t7 = 6
a+2d+a+6d = 6
2a+ 8d =6
a = 6-8d / 2
a= 3- 4d ............(1)

a+2d × a+ 6d. = 8
a^2 +6da +2da +12d^2=8
apply (1),
(3-4d)^2 + 8d (3-4d)+ 12 d^2=8
9+16d^2_24d+24d-32d^2+12d^2=8
-4d^2 +9 =8
-4d^2 = -1
d^2= 1/4
d=1/2 ...........(2)
apply (2)in (1),
a= 3-4d
=3- 4× 1/2
a =1

Sn = n/2 (2a + (n-1)d)
S20=20/2 × (2 + 19×1/2 )
=10 × (23/2)
=5×23
=115