Question

The sum of first n terms of an AP. 54,51,48,....is 513. find n.​

Answer 1

Answer:

54 , 51 , 48, ....

Sn = 513 , a = 54 , d = a2 - a1

d = 51 - 54

d = -3

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

513 = n/2 { 2(54) + (n - 1)-3)

513× 2 = n { 108 - 3n + 3 }

1026 = n { 111 - 3n }

1026 = 111n - 3n²

3n²- 111n + 1026 = 0

n²- 37n + 342 = 0

n²- 19n - 18n + 342 = 0

n(n - 19 ) - 18(n - 19) = 0

n - 18 = 0 n - 19 = 0

n = 18 n = 19

a18 = a+ 17d

= 54 + 17(-3)

= 54 - 51

= 3

a19 = a+ 18d

= 54 + 18(-3)

= 54 - 54

= 0

a19 value is 0 so we are getting 2 values..

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