Question

Choose the correct choice in the following and justify: The $30th$ term of the A.P: $10,7,4,...$is

• A. $97$
• B. $77$
• C. $-77$
• D. $-87$

Answer 1

The correct option is C

$-77$

Explaining the correct option:

We know that the general term of the A.P is $a_n=a+(n-1)d$, Where $\text{'}a\text{'}$is first of the A.P, $d=a_2-a_1$ is a common difference and $\text{'}{a}_n\text{'}isthenthterm.$

The given A.P is $10,7,4,...$

First-term is $a=10$, Common difference is $d=7-10=-3$ and $n=30$.

Putting all the above values in the general form we get:

$$\begin{gathered} \Rightarrow a_{30}=10+(30-1)(-3) \\ \Rightarrow a_{30}=10+\left(29\right)(-3) \\ \Rightarrow a_{30}=10-87 \\ \Rightarrow a_{30}=-77 \end{gathered}$$

Hence, option C is correct.