The seventh term of an arithmetic sequence is $- 16$ and the tenth term is $- 31$
) Find the twenty-fourth term
A) $a _ { 24 } = - 101$
B) $a _ { 24 } = - 66$
C) $a _ { 24 } = - 55$
D) $a _ { 24 } = - 201$
E) $a _ { 24 } = - 51$

Question

Quizplus · Accepted Answer

We first need to find the common difference, denoted by $d$. Let $a_1$ be the first term of the sequence. We know that $a_7 = -16$ and $a_{10} = -31$, so we can set up the following equations:

\begin{align*}
a_7 &= a_1 + 6d = -16 \
a_{10} &= a_1 + 9d = -31
\end{align*}

We can subtract the first equation from the second to eliminate $a_1$ and get:

$$3d = -15 \Rightarrow d = -5$$

Now we can use this common difference to find $a_{24}$:

\begin{align*}
a_{24} &= a_{10} + 14d \
&= -31 + 14 (-5) \
&= -101
\end{align*}

Therefore, the answer is $\boxed{	ext{(A) }a_{24} = -101}$.

The Seventh Term of an Arithmetic Sequence Is −16- 16−16 And the Tenth Term Is

The Seventh Term of an Arithmetic Sequence Is $- 16$ And the Tenth Term Is