Question

Evaluate the arithmetic series described:

a (subscript 1) = 12
a (subscript n) = 64
Find S (subscript 14)

Answers:
541
532
1082
1064
...the subscript thing isn't working for some reason

Answer 1

532

Explanation:

Sum of the first n terms of an arithmetic series:

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

Where:

• aₙ is the nth term.
• a₁ is the first term.
• n is the position of the term.

Given terms:

• 
  `a_1=12`
• 
  `a_n=64`

Substitute the given terms into the formula to create an equation for the nth term:

`\implies S_n=(n)/(2)(12+64)`

`\implies S_n=(n)/(2)(76)`

`\implies S_n=38n`

To find S₁₄, substitute n = 14 into the found equation:

`\begin{aligned}n=14 \implies S_(14)&=38(14)\\ & = 532\end{aligned}`