What is the 24th term of the arithmetic sequence where a1 = 8 and a9 = 56 ?

use \[\large A_n = A_1 + (n-1)d\] where An = A9 A1 = first term n = number of terms (9 in this case) d = this is what you're gonna look for

so An=16d? how is that suppose to work?

16d? you're supposed to have \[\large A_9 = 8 + (9-1)d\]

then A9 = 56 \[\large 56 = 8 + 8d\]

got it?

okay so 6

\[8 = a + (1-1) d\] dats your equation 1 then from dat u can see that a = 8 and this is your first term

d = 6 correct

use that to find A_24 \[\Large A_{24} = A_1 + (n-1)d\] \[\Large A_{24} = 8 + (24-1)6\]

okay so then what formula do i use , lol nevermind okay one sec

then \[56 = a + (9-1) d\] is your equation 2 and solving this gives d = 6

146?

yup

okay so how do I find d for this one What is the 41st term of the arithmetic sequence where a1 = 17 and a15 = â€“39 ?

same way \[\large A_{15} = A_1 + (n-1)d\]

yeah but idk how you got the formula to find d

you're familiar with \[\large A_n = A_1 + (n-1)d\] right??

yeah but if Idk what d is or how to find it that formula serves me no good

okay...lemme teach you how... \(\large A_n\) is the last term \(\large A_1\) is the first term to find n...you look at the number you used in A_n...whatever the subscript (the small number beside A) is that becomes n d is the common difference...usually it is solved by second term minus first term

I get all of that but in the problem What is the 41st term of the arithmetic sequence where a1 = 17 and a15 = â€“39 i dont know the common, thats what i am getting at and I DONT KNOW HOW to find it.

ahhh i am really sorry that was bad timing for MY CAplock to come on. :/

that's whhy we look for common denominator first

we let A_15 be the last term

so we get \[\large A_{15} = A_1 + (n-1)d\] our first term is17 so that becomes A1...lastt term is -39 so that's A_n...then n is the subscript of A_n which is 15 in this case so... \[\Large -39 = 17 + (15 - 1)d\]

Please find the attached document for a full explained answer

-4 is d

but how did you get -39

-39 is the last term

d = 6, term 1 is 8, term 9 is 56 and the nth term is (6n + 2)...... I do not have a calculator with me and I don't want to count so just plug in 24 in place of n to find term 24

The correct answer was 146! Ty!!