Question

A sequence consists of the positive odd integers 1, 3, 5,... What's the sum of the first 12 terms of the sequence?A) 144B) 115C) 169D) 121

Answer 1

This sequence have a constant difference between consecutive elements, which means it is an arithmetic sequence.

The sum of the elements of an arithmetic sequence is:

`S_A=(n(a_1+a_n))/(2)`

Where "n" is the number of elements, a1 is the first element and an is the nth element.

To get the nth element, we use the formula:

`a_n=a_1+(n-1)d`

Where "d" is the constant difference between consecutive elements.

In this case, we have:

`\begin{gathered} a_1=1 \\ d=2 \\ n=12 \end{gathered}`

So, the nth term is:

`\begin{gathered} a_n=1+(12-1)\cdot2=1+11\cdot2=1+22 \\ a_n=23 \end{gathered}`

And the sum of the first 12 elements is:

`S_A=(12(1+23))/(2)=(12\cdot24)/(2)=6\cdot24=144`

Alternative A.