Question

the sum of first n terms of an ap whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another AP whose first term is -30 common difference is 8 find n

Answer 1

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Answer 2

n = 11

Given:

First term of the Arithmetic Progression (a1) = 8

Common Difference of the Arithmetic Progression (d1) = 20

First term of the Arithmetic Progression (a2) = - 30

Common Difference of the Arithmetic Progression (d2) = 8

Formula to find the sum of n terms of an ap:

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

Substituting the values which are known to us into this formula we get for first AP:

Sn = n/2 (2 x 8 + (n - 1) 20

Sn = n/2 (16 + 20n - 20)

Sn = n/2 (20n - 4)

Sn = n(10n - 2)

Substituting the values which are known to us into this formula we get for the second AP:

Finding the sum of first 2n terms of the AP:

S2n = 2n/2(2 x - 30 + (2n - 1) (8)

S2n = n(-68 + 16n)

From this question we are told that:

Sn = S2n

Equation both which we got:

n(10n - 2) = n(-68 + 16n)

10n - 2 = - 68 + 16n

68 - 2 = 16n - 10n

66 = 6n

n = 66/6

n = 11

Therefore, the value of n is 11.