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Answer each question about the following arithmetic series:
12 + 18 + 24 + 30 + . . . + 198

What is the value of the arithmetic series?

630

1,260

3,360

6,336

Sagot :

MrRoyal

Answer:

(c) 3360

Step-by-step explanation:

Given

The above arithmetic series where:

[tex]T_1 = 12[/tex] --- first term

[tex]d = 6[/tex] --- the common difference (18 - 12 = 6)

[tex]T_n = 198[/tex] --- The last term

Required

The value of the series

First, we calculate n using:

[tex]T_n = T_1 + (n - 1)d[/tex]

This gives:

[tex]198 = 12 + (n - 1)*6[/tex]

Collect like terms

[tex]198 - 12 = (n - 1)*6[/tex]

[tex]186 = (n - 1)*6[/tex]

Divide both sides by 6

[tex]31 = (n - 1)[/tex]

Make n the subject

[tex]n = 31 + 1[/tex]

[tex]n=32[/tex]

The sum of the series is:

[tex]S_n= \frac{n}{2}(T_1 + T_n)[/tex]

So, we have:

[tex]S_n= \frac{32}{2}(12 + 198)[/tex]

[tex]S_n= \frac{32}{2}*210[/tex]

[tex]S_n= 16*210[/tex]

[tex]S_n= 3360[/tex]

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