Question

Find the sum of the arithmetic series 28+28.4+...+42

Don’t understand, am I missing something? See pic.

Answer 1

A. 1260

Explanation:

Given the arithmetic series:

`28+28.4+\ldots+42`

We want to find the sum of the arithmetic series.

Whenever the first and last term of an arithmetic series is given, the sum of the series can be found using the formula:

`S_n=(n)/(2)(a+l)`

• First term, a = 28

,

• Last Term, l = 42

We need to find the value of n.

From the series:

• The first term, a = 28

• The common difference, d = 28.4-28=0.4

Substitute these values into the formula for the nth term of an arithmetic sequence:

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

Substitute the values: an=42, a1=28, and d=0.4

`\begin{gathered} 42=28+(n-1)0.4 \\ 42-28=0.4n-0.4 \\ 14=0.4n-0.4 \\ 14+0.4=0.4n \\ 14.4=0.4n \\ n=(14.4)/(0.4) \\ n=36 \end{gathered}`

The number of terms in the sequence is 36.

Finally, find the sum:

`\begin{gathered} S_(n)=(n)/(2)(a+l) \\ S_(36)=(36)/(2)(28+42)=18*70=1260 \end{gathered}`

The sum of the arithmetic series is 1260.

Option A is correct.