Question

the sum of third and seventh term of an AP is 6 and their product is 8 find sum of first sixteen term of AP​

Answer 1

Answers

So using formula for n th term

a_n=a+(n-1)d

a = first term

n = no. of terms

d = common difference

So given

a + (3-1)d + a (7-1)d = 6

2a + 8d = 6

a + 4d = 3

a = 3 - 4d

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

(3 - 2d)( 3 + 2d) = 8 {substituting a = 3 - 2d}

9 - 4d² = 8

d = +1/2 and - 1/2

so when d = +1/2 then a = 3 - 2 = 1 and when d = -1/2 a = 3 + 2 = 5

so using formula for

S_n=\frac{n}{2}[2a+(n-1)d]

when d = +1/2

S_n=\frac{16}{2}[2*1+(16-1)d]

S_n=76

Similarly when d = -1/2

S_n=20