Question

What is a formula for the nth term of the given sequence? 13,15,17…

Answer 1

Answer:
`a_n = 2n+11`

======================================

Step-by-step explanation:

The gap between adjacent terms is 2.

• 15-13 = 2
• 17-15 = 2

We add 2 to each term to get the next. Therefore, d = 2 is the common difference.

The first term is
`a_1 = 13`

Use that and the value of d to determine the nth term formula of this arithmetic sequence.

`a_n = a_1 + d(n-1)\\\\a_n = 13 + 2(n-1)\\\\a_n = 13 + 2n-2\\\\a_n = 2n+11 \textbf{ is the final answer}\\\\`

---------------

Check:

Plug in n = 1

`a_n = 2n+11\\\\a_1 = 2*1+11\\\\a_1 = 2+11\\\\a_1 = 13\\\\`

That confirms 13 being the 1st term.

Now use n = 2

`a_n = 2n+11\\\\a_2 = 2*2+11\\\\a_2 = 4+11\\\\a_2 = 15\\\\`

That matches with the fact 15 is the 2nd term.

I'll let you check the third term.