Question

If the sum of the first n terms of an AP is given by sn=5n^+3n find the Nth term ofor the AP.

Answer 1

we are given -

Sn = 5n^2 + 3 n

{by formula : sn = n/2 ( 2a + ( n -1 ) d ) }

n / 2 ( 2 a + ( n - 1) d = 5 n ^2 + 3n

n ( 2 a + ( n - 1) d ) = 2 ( 5 n^2 + 3n )

n ( 2 a + ( nd - d ) ) = 10 n ^2 + 6 n

multiplying n with equation

2 an + n^2 d - dn = 10 n^2 + 6 n

comparing coefficients of n^2 as underlined , we get d = 10

comparing coefficient of n -

2an - dn = 6 n ( left equation )

2a - d = 6

2 a - 10 = 6. ( d = 10 )

2 a = 6 + 10

2a = 16

a = 8

nth term :-

an = a + ( n - 1 ) d

an = 8 + ( n -1 ) 10

an = 8 + 10 n - 10

an = 10 n - 2

regrds

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Answer 2

Answer:

10n-2

Step-by-step explanation:

Sn=n÷2(2a+(n-1)d)

use the above formula