jholland03

23.06.2019 •

Mathematics

What is the following sum? 4(5 sqrt x^2y)+3(5 sqrt x^2y) right answer pls unlike the other guy who posted

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Ответ:

lilsneak13

04.09.2022

Mathematics

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:

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

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