Chapter 19, Problem 1RE

To determine

Whether the statement “For an arithmetic sequence, if $a_1=5,d=3\text{ and }n=10$, then $a_{10}=35$” is true or false.

Answer to Problem 1RE

The statement is $\underset{\_}{\text{false}}$.

Explanation of Solution

Definition used:

n terms:

The nth term of the arithmetic sequence is given by $a_n=a_1+\left(n-1\right)d$, where $a_n$ is any term, $a_1$ is the first term and d is the common difference.

Calculation:

It is given that $a_1=5,d=3\text{ and }n=10$.

Substitute $a_1=5,d=3\text{ and }n=10$ in $a_n=a_1+\left(n-1\right)d$ and obtain the value of $a_{10}$ as follows:

$\begin{array}{c}{a}_{10}=a_1+\left(10-1\right)\left(d\right)\\ =5+\left(9\right)3\\ =5+27\\ =32\\ \ne 35\end{array}$

Therefore, the statement is $\underset{\_}{\text{false}}$.