Question

In an ap the sum of first 10 terms is -50 and the sum of its next 10 terms is -250 find the ap

Answer 1

Sum of first 10 terms = -50

Sn = (n/2)[2a + (n-1)d]

S10 = (10/2)[2a + (n-1)d]

S10 = 5[2a + (10-1)d]

-50 = 5[2a + 9d]

2a + 9d = -10

Here sum of terms between 10 and 20 is -250, so sum of first 20 terms = -300

S20 = (20/2)[2a + (20-1)d]

-300 = 10[2a + 19d]

2a + 19d = -30

Solving for a and d :

2a + 19d = -30

2a + 9d = -10

Subtracting second equation from first :

10d = -20

d = -2

Replacing the value of d in second equation :

2a - 18 = -10

2a = 8

a = 4

So the AP is

4, 2, 0, -2, -4, -6, ....