Question

What is the 41st term of the arithmetic sequence where a1 = 17 and a15 = -39 ?

Answer 1

@mathstudent55

Answer 2

well you need to find the common difference... which is the amount the sequence changes by

the formula for a term in an arithmetic sequence is

\[T_{n} = a + (n - 1)\times d\]

n = number of terms, a = 1st term and d = common difference.

to to find the common difference you know the 15th term, n = 15 and a = 17

substitute them to find d

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

or

-39 = 17 + 14d

solve for d.

when you have it then use n = 41, a = 17 and your value of d in the formula to find the 41st term

Answer 3

d is -4

Answer 4

the Tn formula?

Answer 5

correct...

now just go back to the formula to find the 41st term a = 17 and n = 41