Question

Answer each question about the following arithmetic series:

Answer 1

Answer:

(c) 3360

Step-by-step explanation:

Given

The above arithmetic series where:

$T_1 = 12$ --- first term

$d = 6$ --- the common difference (18 - 12 = 6)

$T_n = 198$ --- The last term

Required

The value of the series

First, we calculate n using:

$T_n = T_1 + (n - 1)d$

This gives:

$198 = 12 + (n - 1)*6$

Collect like terms

$198 - 12 = (n - 1)*6$

$186 = (n - 1)*6$

Divide both sides by 6

$31 = (n - 1)$

Make n the subject

$n = 31 + 1$

$n=32$

The sum of the series is:

$S_n= \frac{n}{2}(T_1 + T_n)$

So, we have:

$S_n= \frac{32}{2}(12 + 198)$

$S_n= \frac{32}{2}*210$

$S_n= 16*210$

$S_n= 3360$

Answer 2

Answer:

c

Step-by-step explanation: