Find the first four terms of the sequence defined by the explicit rule f(n)=7(n-1)-10. Is it an arithmetic sequence?

1 Answer
May 1, 2018

Yes

Explanation:

Explicit rules for arithmetic sequences follow the format #a_n=d(n-1)+a_1# (or with a #f(n)# instead of an #a_n#), where #d# represents the common difference and #a_1# represents the first term

To find the first 4 terms, plug #1, 2, 3, 4# in for #n#:

#f(1)=7(1-1)-10#

#f(1)=7(0)-10#

#f(1)=0-10#

#f(1)=-10#

Do the same thing for #2, 3, 4#

The first four terms are #-10, -3, 4, 11#