Mathematics
OpenStudy (anonymous):

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

OpenStudy (lgbasallote):

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

OpenStudy (anonymous):

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

OpenStudy (lgbasallote):

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

OpenStudy (lgbasallote):

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

OpenStudy (lgbasallote):

got it?

OpenStudy (anonymous):

okay so 6

OpenStudy (anonymous):

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

OpenStudy (lgbasallote):

d = 6 correct

OpenStudy (lgbasallote):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

146?

OpenStudy (lgbasallote):

yup

OpenStudy (anonymous):

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

OpenStudy (lgbasallote):

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

OpenStudy (anonymous):

yeah but idk how you got the formula to find d

OpenStudy (lgbasallote):

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

OpenStudy (anonymous):

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

OpenStudy (lgbasallote):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (lgbasallote):

that's whhy we look for common denominator first

OpenStudy (lgbasallote):

we let A_15 be the last term

OpenStudy (lgbasallote):

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... \[\Large -39 = 17 + (15 - 1)d\]

OpenStudy (anonymous):

OpenStudy (anonymous):

-4 is d

OpenStudy (anonymous):

but how did you get -39

OpenStudy (lgbasallote):

-39 is the last term

OpenStudy (anonymous):

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

OpenStudy (anonymous):

The correct answer was 146! Ty!!