Question

The sum of the third and seventh term of an A.P. is 6 and their product is 8. Find the sum of first sixteen terms of the A.P.?

Answer 1

SOLUTION⬆️

REFER TO THE ATTACHMENT.

Hope it helps ☺️

Answer 2

Answer:

76

Step-by-step explanation:

The sum of 3rd and 7th terms are 6 and product is 8.

SO we can form a quadratic equation as $x^{2}  - 6x + 8 = 0$

(x - 2)(x - 4) = 0

x = 2 or 4

So let the 3rd term = 2 = a + 2d

and 7th term = 4 = a + 6d

7th term - 3rd term = (a + 6d) - (a + 2d) = 4 - 2

4d = 2

d = 1/2

So, 3rd term = a + 2*1/2 = 2

a + 1 = 2

a = 1

so, Sum of first 16 terms = n/2*(2a + (n-1)*d) = 16/2 * (2*1 + 15*1/2) = 76