Question

what is the sum of the arithmetic sequence 17,13,9... if there are 40 terms ?

Answer 1

we can either find the 40th term or use the set up for the 40th term; either way is suitable

Answer 2

an = a1 + d(n-1)

where a1 is the first term; d is the difference between terms; and n is the nth term we want

Answer 3

okay

Answer 4

so help me out; our first term (a1) is?

Answer 5

17?

Answer 6

yes

and since we want the nth term to be 40 lets go ahead and use that as well

a40 = 17 + d(40-1)

all we need now is the "d"

17 + d = 13 should suffice

Answer 7

d= 4

Answer 8

well, -4 :)

17 + (-4) = 13 ...

sooo

a40 = 17-4(39) is what we need to use in the summation formula that i presented last time

Answer 9

a40 = -139 if my calculator hasnt lied to me

so lets fill in the summation with these:

\[S=\frac{n(a_1+a_{40})}{2}\]
\[S=\frac{40(17-139)}{2}\]

Answer 10

-2440

Answer 11

-2440, i agree

Answer 12

thanks

Answer 13

youre welcome