Question

Find the sum of 12 terms of an A.P. whose nth term is given by an = 3n + 4

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Answer 1

Answer:

hope this is helpful to you.........

Answer 2

Answer:

The question is from the topic of Arithmetic progression where we are given with an and we have find the sum of 12 terms.

GiveN:

• an = 3n + 4

To find the sum of 12 terms of the AP.....?

So, let's start solving....

First of all, to find the value of 1st term, we need to put the value of n as 1, similarly n = 2, 3......

• a1 = 3(1) + 4 = 7

• a2 = 3(2) + 4 = 10

So the first term of the AP is 7 and second term is 10. Then common difference is the difference between two consecutive terms because it is an arithmetic progression.

$\sf{ \longrightarrow{d = a_2 - a_1}}$

Plug in the values,

$\sf{ \longrightarrow{d = 10 - 7 = 3}}$

Now we have got our first term and common difference, So let's find the sum of 12 terms (n = 12)

$\sf{ \longrightarrow{S_n = \dfrac{n}{2} \bigg(2a + (n - 1)d \bigg)}}$

Plug in the values in the formula,

$\sf{ \longrightarrow{S_{12} = \dfrac{12}{2} \bigg(2 \times 7 + (12 - 1)3 \bigg)}}$

$\sf{ \longrightarrow{S_{12} = 6(14 + 33)}}$

$\sf{ \longrightarrow{S_{12 }= 6 \times 47}}$

$\sf{ \longrightarrow{S_{12} = 282}}$

Hence the required sum of 12 terms of the AP with the above given first term and Common difference is:

$\large{ \boxed{ \sf{ \pink{282 \: (Answer)}}}}$

And we are done !!