Question

PLZ HELP! 20 POINTS!

Answer 1

Answer:

a) The error is that, the initial value is n=1 NOT n=3

b) The sum is $a_n=a_{n+1}+5=192$

c)The explicit formula is  $a_n=5n+3$

The recursive formula is $a_n=a_{n+1}+5$,

Step-by-step explanation:

The given arithmetic series is  8 + 13 + ... + 43.

The first term is $a_1=8$, the  common difference is $d=13-8=5$

The nth term is given by:

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

We substitute the values to get:

$a_n=8+5(n-1)\\a_n=8+5n-5\\\\a_n=3+5n$

To find how many terms are in the sequence we solve the equation:

$3+5n=43\\\implies 5n=43-3\\5n=40\\n=8$

The summation notation is  $\sum_{n=1}^8(3+5n)$

The error the student made is in the initial value.

It should be n=1 NOT n=3

b) The sum of the arithmetic series is calculated using:

$S_n=\frac{n}{2}(a+l)$

We substitute o get:

$S_8=\frac{8}{2}(5+43)$

$S_8=4(48)$

$S_8=192$

c) The explicit formula we already calculated in a), which is $a_n=3+5n$

The recursive formula is given as:

$a_n=a_{n+1}+d$

We substitute d=5 to get:

$a_n=a_{n+1}+5$