Question

Find the sum of the arithmetic series.

Answer 1

The first 100 terms of the series 4 + 7 + 10 + 13 +...

Answer 2

@yrelhan4

Answer 3

can you find the common difference between the terms ?

Answer 4

3?

Answer 5

yes!
and 1st term = a1 = 4
number of terms = n =100
use this formula
\(\Large S_n = (n/2)(2a+(n-1)d)\)

Answer 6

where d is the common difference = 3

Answer 7

how do I use the formula they gave me which is Theorem 1... \[S_{n}= \frac{ n(t_1+t_n) }{ 2 }\]

Answer 8

then you need to find 100th term first

Answer 9

yeah that's what I'm having trouble with.

Answer 10

using the formula
\(\Large t_n = t_1 +(n-1)d\)

Answer 11

where, n = 100
t1 = 1st term = 4
d= 3

Answer 12

so that equals 301.

Answer 13

and now I use theorem 1?

Answer 14

yes :)

Answer 15

okay let me try it and I'll hopefully get the right answer.

Answer 16

one second

Answer 17

take your time :)

Answer 18

15,250?

Answer 19

thats correct! :)

Answer 20

\[S_{100}=15,250\]

Answer 21

yes :)

Answer 22

Thank you! :D

Answer 23

welcome ^_^