Question

What is the sum of the arithmetic sequence 3, 9, 15..., if there are 22 terms?

1,452
1,728
2.028
2,268

Answer 1

\[
a_1=3\\
a_n= a_{n-1} +6
\]

Answer 2

Here are the first 22 elements
{3, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 87, 93, 99, \
105, 111, 117, 123, 129}
You can sum them or you can use the formula.

Answer 3

Their sum is
1452
I will explain it to you very soon

Answer 4

You can show that
\[
a_n= 3 + 6(n-1),\, n =1, 2,\cdots 22
\]

Answer 5

\[

\sum_{n=1}^{22} a_n=\sum_{n=1}^{22} (3 + 6(n-1)= 6 (22) + 6 \frac {(21)(22)}2=1452
\]