Question

Find the 15^th term in the arithmetic sequence -3, 4, 11, 18, ….

Short answer

The 15th term in the arithmetic sequence is 95.

Step-by-step solution

Step 1. Given Information.

Given arithmetic sequence is -3, 4, 11, 18, ….

Step 2. Calculation.

The n^th term of an arithmetic sequence is given by $a_n=a_1+(n-1)d$.

Here the first term is $a_1=-3$

The difference between the first two terms is $\begin{array}{c}4-(-3)=4+3\\ =7\end{array}$

The difference between the next two terms is $11-4=7$

Hence, the common difference is $d=7$

And the required term is $n=15$

Plugging the values in the formula:

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_{15}=-3+(15-1)\left(7\right)\\ a_{15}=-3+\left(14\right)\left(7\right)\\ a_{15}=-3+98\\ a_{15}=95\end{array}$

Step 3. Conclusion.

Hence, the 15th term of the arithmetic sequence is 95.