Question

I need help solving this

Answer 1

Given:

`108,105,102,...,15`

This is an arithmetic sequence because it has a common difference.

From the nth term of an arithmetic sequence,

`\begin{gathered} a_n=a+(n-1)d \\ a=108 \\ d=105-108=102-105=-3 \\ a_n=15 \\ \\ Hence,\text{ the number of terms in the sequence is;} \\ 15=108+(n-1)-3 \\ 15-108=-3(n-1) \\ -93=-3(n-1) \\ (-93)/(-3)=n-1 \\ 31=n-1 \\ 31+1=n \\ 32=n \\ n=32 \end{gathered}`

The sum of an arithmetic sequence is given by;

`\begin{gathered} S_n=(n)/(2)(a+l) \\ \\ where: \\ first\text{ term, }a=108 \\ last\text{ term, }l=15 \\ n=32 \\ \\ Hence, \\ S_n=(32)/(2)(108+15) \\ S_n=16(123) \\ S_n=16*123 \\ S_n=1968 \end{gathered}`

herefore, the sum oft the sequence is 1968