Question

Can someone please help me thsi the only one i need

Answer 1

Answer:

a) The explicit formula is $a_n=7n+5$

b) The 31st term of the sequence is 222

Step-by-step explanation:

a) The explicit formula for an arithmetic sequence is:

$a_n=a_1+(n-1)d$

The recursive formula for the sequence is

$a_1=12\\a_n=a_{n-1}+7$

From this formula we can find the common difference by comparing to the general recursive formula:$\\a_n=a_{n-1}+d$

This means the common difference d=7.

We now substitute the first term $a_1=12$ and the common difference $d=7$  into the explicit formula: $a_n=a_1+(n-1)d$ to obtain:

$a_n=12+(n-1)\times 7$

Expand to get:

$a_n=12+7n-7$

Simplify:

$a_n=7n+5$

b) To find the 31st term of this sequence, we substitute n=31 in to the the explicit formula, $a_n=7n+5$  to obtain:

$a_{31}=7*31+5$

Multiply to get:

$a_{31}=217+5$

Add to get:

$a_{31}=222$

Therefore the 31st term of the sequence is 222