Question

2. Find the sum of the geometric series.

Answer 1

`\\ \rm\Rrightarrow \sum^(18)_(n=1)2n-1`

`\\ \rm\Rrightarrow 2(1)-1+2(2)-1\dots+2(18)-1`

• a=2-1=1
• a_18=l=36-1=35

So

`\\ \rm\Rrightarrow S_n=(n(a+l))/(2)`

`\\ \rm\Rrightarrow S_n=(18(1+35))/(2)=9(36)=324`

Answer 2

324

Explanation:

** The attachment shows an arithmetic sequence **

Sum of Arithmetic Series formula

`S_n=\frac12n(a+l)`

where:

• a = initial term
• l = last term

`a_n=2n-1`

`\implies a_1=2(1)-1=1`

`\implies a_(18)=2(18)-1=35`

`\implies S_(18)=\frac12(18)(1+35)=324`