Find the 65 th term of this
arithmetic sequence.

Hint:

Ask by Pearson Potter. in the United States

Mar 28,2025

Question

Find the 65 th term of this arithmetic sequence. $$ 2,10,18,26,34, \ldots $$ $$ a_{65}=[?] $$ Hint: $$ a_{n}=a_{1}+(n-1) d $$

UpStudy AI · Accepted Answer

1. Identify the first term and the common difference:
   - First term: $$ a_{1} = 2 $$
   - Common difference: $$ d = 10 - 2 = 8 $$

2. Use the formula for the $$n$$th term:
   $$
   a_{n} = a_{1} + (n-1)d
   $$

3. Substitute the given values for $$n = 65$$:
   $$
   a_{65} = 2 + (65-1) \cdot 8 = 2 + 64 \cdot 8
   $$

4. Calculate $$64 \cdot 8$$:
   $$
   64 \cdot 8 = 512
   $$

5. Add to find $$a_{65}$$:
   $$
   a_{65} = 2 + 512 = 514
   $$

Thus, the 65th term is $$ a_{65} = 514 $$.
The 65th term is 514.

Find the 65 th term of this
arithmetic sequence.

Hint: