Question

10. The fifth term of an arithmetic sequence is 11 and the tenth term is 41. What is the first term? ​

Answer 1

-13

Explanation:

"Arithmetic sequence" is a big clue, because it means you add on the same amount every time the term number goes up by 1, then add on the same amount to the numbers in the sequence (the list of numbers) see image There are of course formulas to find these missing numbers, but also, crunch it out sometimes so that it makes sense. And when the numbers in the question get crazy you can fall back on the formulas.

Answer 2

`a_(5)=a+4d=11\\a_(10)=a+9d=41`

Solve the above equations,

`a_(10)-a_(5)=41-11\\a+9d-a-4d=30\\5d=30\\d=6\\a=11-24=-13`

First term is -13.