Question

Which expression defines the given series for seven terms?

15 + 19 + 23 + . . . Using the [E]

Answer 1

do you mean using \(\large\color{blueviolet}{ \displaystyle \sum_{ }^{ } }\) ?

Answer 2

your difference is 4 (that is what you are adding every time to find the next term)
your first term term is 15.

\(\LARGE\color{blueviolet}{ \displaystyle \sum_{{\large n{\Large =}{\rm start~plugging~from } }}^{ {\large {\rm number~of~terms} }} ~ {\rm the~pattern}}\)

Answer 3

what can you tell me so far ?

Answer 4

15+19+23+ ... ( 27,31,35)

Answer 5

you don;t need to find those terms

Answer 6

I will give you an example of how to write a pattern.

Sequence:
\(\large\color{blueviolet}{ \displaystyle 4,~~~9,~~~14,~~~19,~~~...}\)

write the expression that will represent 100 terms.
You know that
\(\large\color{blueviolet}{ \displaystyle a_1=4}\)
\(\large\color{blueviolet}{ \displaystyle d=5}\)

\(\large\color{blueviolet}{ \displaystyle \sum_{ n=0 }^{ 99 } ~(5n+4)}\)

Answer 7

you plug in n=0 for the first term (and get 4)
plug in n=1 for the second term (and get 9) and on...
you will have n=99 for 100th term.

so it grows by 5, or in other words, the slope is 5.
And the a(1)=4, in other words y-intercept is 4.

Answer 8

is this example making sense ?

Answer 9

so d is the number of how many times is adding up ?