Question

in ap the sum of first 10 terms is - 150 and sum of next 10 terms is - 550,find ap

Answer 1

S10 = -150

S20 - S10 = - 550
S20 = - 550 + S10
S20 = - 700

Sn = (n/2) * [2a + (n - 1)]d
S10 = (10/2) * (2a + 9) = - 150
S20 = (20/2) * (2a + 19d) = - 700

2a + 9d = - 30
2a + 19d = - 70
=> d = -4, a = 3

An = 3 + (n - 1) * (-4)
An = - 4n + 7

Answer 2

According to question
S10 = - 150
10/2 [ 2a +(10-1)d] = - 150
=> 5(2a +9d) = - 150
=> 2a +9d = - 30 -----------(1)

And,
S20-S10 = - 550
=> 20/2[ 2a +(20-1)d] - (-150) = - 550
=> 10(2a +19d)+150= - 550
=> 10(2a +19d) = - 700
=> 2a + 19d = - 70 ----------(2)

Subtracting equation 1 from 2, we get

10d = - 70+30
10d = - 40
d = - 4

On putting the value of d in equation 1, we get
2a-36= - 30
=> 2a = 6
=> a = 3

Ap will be 3,-1,-5,-9............


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