Question

The sum of 7 terms of an A.P is equal to the sum of 13 terms of an same A.P. then sum of 20 terms of same A.P​

Answer 1

7/2 (2a+6d) = 13/2 (2a+12d)

7a+21d = 13a+78d

6a + 57d = 0

2a + 19d = 0

S20 = 20/2 (2a+19d) = 0

Use the formula for the sum of terms

(7/2)(2a + 6d) = (13/2)(2a + 12d)

times 2, then expand

14a + 42d = 26a + 156d

-12a = 114d

a = -19/2 d

sum(20) = 10(2a + 19d)

= 20a + 190d

= 20(-19/2 d) + 190d

= 0

Answer 2

Answer:

The sum of 7 terms of an A.P is equal to the sum of 13 terms of an same A.P. then sum of 20 terms of same A.P