Question

find an arithmetic sequence if a15= -22 and a23=42

Answer 1

\[\large a_{15}=-22\]
\[\large a+(n-1)d=-22\]
\[\large a+(15-1)d=-22\]
\[\large a+14d=-22\]
\[\large a_{23}=42\]
\[\large a+(n-1)d=42\]
\[\large a+(23-1)d=42\]
\[\large a+22d=42\]
Solve simultaneously
\[\large a+14d=-22[1]\]
\[\large a+22d=42[2]\]
\[[2]-[1]\]
\[\large (a+22d)-(a+14d)=(42)-(-22)\]
\[\large 22d-14d=42+22\]
\[\large 8d=64\]
\[\large d=8\]
FInd a by subbing the d-value into one of the two equations above.
\[\large a+14d=-22[1]\]
\[\large a+14(8)=-22\]
\[\large a=-22-112\]
\[\large a=-134\]

Answer 2

"a" is the first term. "d" is the common difference. SO now you can set up an arithmetic sequence.

Answer 3

so how would i set it up after this. would i start from a15?

Answer 4

Nope, you start from the first term which is "a" and then you write 2 more numbers after that using the "d" (common difference). The question doesn't even state how many terms there are, so you just write the first three terms unless you didn't write the full question down...