Question

If the sum of n terms of an AP is 2n² + 5n, then its nth term is​

Answer 1

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Sum of 1 terms = a = 2(1)² + 5(1)

=2+5=7

Sum of 2 terms =

a+a2 = 2(2)² + 5(2)

a2 = 8 + 10 - 7

a2=11

d= a2 - a=11-7 = 4

a'n =a +(n-1)d = 7 +(n-1)4

a'n= 7+4n-4 = 3+4n

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...Hope it helps....

Answer 2

$S_{n}$ = 2n² + 5n

Take n = 1

=> $S_{1}$ = 2(1)² + 5(1)

=> 2 + 5

=> 7

Take n = 2

$S_{2}$ = 2(2)² + 5(2) - 7

=> 8 + 10 - 7

=>18 - 7

=> 11

Take n = 3

$S_{3}$ = 2(3)² + 5(3) - 18

=> 18 + 15 - 18

=> 15

AP : 7, 11, 15 ....

Now,

We have to find the nth term of an AP.

So,

$a_{n}$ = a + (n - 1)d

We have

• First term (a) = 7
• Common difference (d) = 11 - 7 = 4

So,

$a_{n}$ = 7 + (n - 1)4

=> 7 + 4n - 4

=> 3 + 4n

∴ 3 + 4n is the nth term of an AP.