Question

The sum of the third and the seventh term of an ap is 6 and their product is eight find the sum of first sixteen terms of ap

Answer 1

Hello user !

Answer :

Let the first them be a and common difference be d.

GIVEN: a3 +a7 = 6

Therefore, a + (3-1) * d + a + (7-1)*d = 6

a + 2d + a + 6 d = 6

2a + 8d = 6 ( Dividing both sides by 2)

a + 4 d = 3

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

And , also given : product of third and seventh term is 8

So,( a + 2d )*(a+6d) = 8

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

putting value of (a )in above eq.

(3-4d) ^2 +8ad +12d ^2= 8

Above is mentioned in the picture

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