Question

If the nth term of AP is 3N +5 find the sum of first 12 terms

Answer 1

according your question

after calculation We find the first term of Ap is =8
and diff is =3
so the sum of first 12term of this Ap is
n/2(2a+(n-1)*d so 12/2(2*8+(12-1)*3=
answer is=294
I hope it's a right answer of your question.

Answer 2

Given,

The nth term of AP is 3N +5.

To Find,

The sum of the first 12 terms =?

Solution,

We can solve the question using the following steps:

It is given that the nth of the AP is 3N + 5.

$T_{N} = 3N + 5$

We know that the nth term of an AP is given as:

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

Therefore,

$a + (N - 1)d = 3N + 5$

$dN + a - d = 3N + 5$

Comparing coefficients on both sides,

$d = 3, a - d = 5$

Substituting the value of d,

⇒$a = 5 + 3 = 8$

Therefore,

common difference, $d = 3$

first term, $a = 8$

Now,

Sum of n terms in AP $= \frac{N}{2} (2a + (N - 1)d)$

Substituting the values,

$= \frac{12}{2} (2*8 + (12 - 1)3)$

$= 6(16 + 33)$

$= 294$

Hence, the sum of the first 12 terms is 294.