Question

1. if the sum of 8 terms of an ap is 64 and the sum of 19 terms is 361. find the sum of n terms.

Answer 1

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Answer 2

Answer:

First term of the progression is 1 and common difference of the progression is 2

Step-by-step explanation:

Sum of the 8 terms of an arithmetic progression = 64

Since sum of n terms of an arithmetic progression is represented by

$S_{n}=\frac{n}{2}[2a+(n-1)d]$

$64=\frac{8}{2}[2a+(8-1)d]$

64 = 4[2a + 7d]

16 = 2a + 7d ------(1)

Sum of 19 terms of the progression = 361

$S_{n}=\frac{n}{2}[2a+(n-1)d]$

$361=\frac{19}{2}[2a+(19-1)d]$

19[a + 9d] = 361

a + 9d = 19 ------(2)

Equation (2)×2 - (1)

2(a + 9d) - (2a + 7d) = 38 - 16

2a + 18d - 2a - 7d = 22

11d = 22

d = 2

From equation (2)

a + 18 = 19

a = 19 - 18 = 1

Therefore, First term of the progression is 1 and common difference of the progression is 2.

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