Question

What is the sum of the arithmetic sequence 6, 14, 22,
if there are 26 terms

Answer 1

do you know the formula to find any term in the sequence?

Answer 2

isnt it like an=a1(r)^2-1?

Answer 3

it "like" that yes, but that ones looks more like the GEOmetric sequence formula
the one for arithmetic is:

an = a1 + d(n-1)

Answer 4

ok so what do I do?

Answer 5

you have a1, you know how to find any term now, and you want the 26th term. All your missing is the common difference "d" between each term.

but, your given 3 terms to begin with, so number do you have to add to the firs term to get the second term?

a1 + d = a2

Answer 6

the difference is 8 so what do i do now?

Answer 7

we have all the pieces we need to find the 26th term, then we can find the sum

Answer 8

a26 = 6 + 8(26-1)

Answer 9

a26=206?

Answer 10

yes

Answer 11

how we have all the parts we need for the next formula

n(a1 + a26)/2 ; where n = 26 and we know a1 and a26

26(6+208)/2

Answer 12

206 .... not 208 :)

Answer 13

26(6+206)/2 = 26(3+103) = 26(106)

Answer 14

so it 2782?

Answer 15

wait no what is it?

Answer 16

ooooo 2756

Answer 17

i get 2756 with the correct values :)

Answer 18

it simpler when you know why the formulas work, they realy are quite intuitive. but if all you see is a formula and have to memorize the formula, it can be challenging

Answer 19

THANKS:)

Answer 20

youre welcome