Find the first five terms of the recursive sequence. Show all work. $$ a_{n}=a_{n-1}+7 $$ where $$ a_{1}=5 $$

Question

UpStudy AI · Accepted Answer

1. The recursive formula is given by 
   $$
   a_n = a_{n-1} + 7
   $$
   with the initial term 
   $$
   a_1 = 5.
   $$

2. Find $$ a_2 $$:
   $$
   a_2 = a_1 + 7 = 5 + 7 = 12.
   $$

3. Find $$ a_3 $$:
   $$
   a_3 = a_2 + 7 = 12 + 7 = 19.
   $$

4. Find $$ a_4 $$:
   $$
   a_4 = a_3 + 7 = 19 + 7 = 26.
   $$

5. Find $$ a_5 $$:
   $$
   a_5 = a_4 + 7 = 26 + 7 = 33.
   $$

The first five terms of the sequence are:
$$
5, \; 12, \; 19, \; 26, \; 33.
$$
The first five terms of the sequence are 5, 12, 19, 26, and 33.

Find the first five terms of the recursive sequence. Show all work. \( a_{n}=a_{n-1}+7 \) where \( a_{1}=5 \)