Question

The first term of an arithmetic sequence is 14. The 25th term is 206. find the common difference

Answer 1

We can manipulate the arithmetic sequence formula to solve this problem.

Let's look at $a_{n} = a_{1} +(n-1)d$ where $a_{n}$ is the $n^{th}$ term, $a_{1}$ is the first term, $n$ is the number of terms, and $d$ is the common difference. We already know that $a_{1}$ is equal to $14$, $n$ is equal to $25$, and $a_{25}$ is equal to $206$. This therefore leave us with only the common difference to solve.

Manipulating the formula we can arrive at the answer:
$206 = 14 +(25-1)d$
$192 = (24)d$
$d=8$

ANSWER: The common difference is 8.