Question

What is the 41st term of the arithmetic sequence where a1 = 15 and a15 = -41 ?


-157

-153

-149

-145

Answer 1

a15 = -41
a1+(14)d=-41
15+14d=-41
d=-4

a41=a1+(40)d
a41=(15)+40(-4)=?

Answer 2

use the 15th term to find the common difference

\[-41 = 15 +(15 -1)d\]

or

\[-41 = 15 + 14d\]

then the equation for a term in an arithmetic sequence is

\[T _{n} = a +(n -1)d\]

where n = 41, a = 15 and d was calculated above