Question

Find the 11th term of the A.P. $-5,-\frac{5}{2},0,\frac{5}{2}....$

Answer 1

Step1: Calculating the common difference $d$:

Subtract the first term from the second term of the given A.P. we get,

$$\begin{gathered} d=-\frac{5}{2}-(-5) \\ \Rightarrow d=-\frac{5}{2}+5 \\ \Rightarrow d=\frac{-5+10}{2} \\ \therefore d=\frac{5}{2} \end{gathered}$$

Step2: Calculating the 11^th term $a_{11}$:

The n_th term of an A.P. is given by the formula $a_n=a+(n-1)d$, where $a$ is the first term of the A.P. and $d$ is the common difference.

Substituting the value of $n$ as 11, $a$ as $-5$ and $d$ as $\frac{5}{2}$ we get,

$$\begin{gathered} a_{11}=-5+(11-1)\frac{5}{2} \\ \Rightarrow a_{11}=-5+\left(10\right)\frac{5}{2} \\ \Rightarrow a_{11}=-5+25 \\ \therefore a_{11}=20 \end{gathered}$$

Final Answer: The 11th term of the given A.P. series is 20.