Question

Need help with question number eight. Describe arithmetic series described

Answer 1

Given the arithmetic series below

`6+8+10+12+\cdots,\text{ n = 8}`

To find the sum of the arithmetic series,

We find the last term, i.e 8th term of the series

The formula to find the last term/formula for the arithmetic progression is given below

`U_n=a+(n-1)d`

The common difference, d, is

`2nd\text{ term - 1st term = 8 - 6 = 2}`

Where,

`n=8,d=2,a=6`

Substitute the values into the formula to find the 8th term

`\begin{gathered} U_8=6+(8-1_{})(2)=6+(7)(2)=6+14=20 \\ U_8=20 \end{gathered}`

The formula to find the arithmetic series is

`S_n=(n)/(2)(a_1+a_n)_{}`

Where

`a_1=6,n=8,a_8=U_8=20`

Subtsitute the values into the formula to find the arithmetic series above

`\begin{gathered} S_8=(8)/(2)(6+20)=4(26)=104 \\ S_8=104 \end{gathered}`

Hence, the sum of the arithmetic series is 104