Question

The sum of the third and the seventh terms of an A.P is 6 and their product is 8. Find the sum of first 20 terms of the A.P​

Answer 1

Answer:

115

Step-by-step explanation:

let the first term of the ap be a and let the common difference be d.

the third term : a + (3-1) d = a + 2d _______ a

the seventh term : a + ( 7-1 ) d = a + 6d _________b

adding a and b, we get

a + 2d + a + 6d = 2a + 8d = 6

                        a = 6 - 8d/2 = 3-4d

a + 2d x a + 6d = (3-4d + 2d) x ( 3-4d + 6d) = 8

                          = (3 - 2d) x (3 + 2d)

                          = 9 - 4d^2 = 8

                           4d^2 = 1

                            d^2 = 1/4

                            d = + 1/2 or - 1/2

therefore, a = 3 - 4x 1/2 = 1

the sum of first 20 terms = 20/2 x ( 2x1 + ( 20 -1 ) x 1/2 )

= 10 x ( 2 + 19/2) = 10 x ( 4+ 19/2 )

= 5 ( 23 )

= 115

hope it helps.

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