Question

If for an a p ,the first term is 3 and the common difference is 6 then find sn

Answer 1

here is ur answer:


1st term = a = 3

common difference = d = 6

now sn:



$s_{n} = \frac{n}{2} (2a + (n - 1)d) \\ \\ s_{n} = \frac{n}{2} (2 \times 3 + (n - 1)6) \\ \\ s_{n} = \frac{n}{2} (6 + 6n - 6) \\ \\ s_{n} = \frac{n}{2} (6n) \\ \\ s_{n} = \frac{6 {n}^{2} }{2} \\ \\ s_{n} =3 {n}^{2}$




hope it helps you!
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Answer 2

Answer:

1st term = a = 3

common difference = d = 6

now sn:

\begin{gathered}s_{n} = \frac{n}{2} (2a + (n - 1)d) \\ \\ s_{n} = \frac{n}{2} (2 \times 3 + (n - 1)6) \\ \\ s_{n} = \frac{n}{2} (6 + 6n - 6) \\ \\ s_{n} = \frac{n}{2} (6n) \\ \\ s_{n} = \frac{6 {n}^{2} }{2} \\ \\ s_{n} =3 {n}^{2}\end{gathered}

s

n

=

2

n

(2a+(n−1)d)

s

n

=

2

n

(2×3+(n−1)6)

s

n

=

2

n

(6+6n−6)

s

n

=

2

n

(6n)

s

n

=

2

6n

2

s

n

=3n

2