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in Arithmetic Progression by (44.5k points)
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If the sum of 8 terms of an A.P. is 64 and the sum of 19 terms is 361, find the sum of n terms.

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Given: S8 = 64 and S19 = 361

We know that,

⇒ 38 = 2a + 18d …(ii)

Solving linear equations (i) and (ii), we get

2a + 7d – 2a – 18d = 16 – 38

⇒ -11d = -22

⇒ d = 2 …(iii)

Putting the value of d in eq. (i), we get

2a + 7(2) = 16

⇒ 2a = 16 – 14

⇒ 2a = 2 …(iv)

Now, we have to find the Sn

[from (iii) and (iv)]

⇒ Sn = n [1 + n – 1]

⇒ Sn = n2

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