Question

Find the common difference $d$ and write three more terms of an $AP$:

$2,\frac{5}{2},3,\frac{7}{2}$

Answer 1

$2,\frac{5}{2},3,\frac{7}{2},.....$

$\Rightarrow$ Difference between second and first term $=\frac{5}{2}-2=\frac{5-4}{2}=\frac{1}{2}$

$\Rightarrow$ Difference between third and second term $=3-\frac{5}{2}=\frac{6-5}{2}=\frac{1}{2}$

$\Rightarrow$ Difference between fourth and third term $=\frac{7}{2}-3=\frac{7-6}{2}=\frac{1}{2}$

Since difference is same, it is an $AP$

$\Rightarrow$ Common difference $=d=\frac{1}{2}$

$\Rightarrow$ Now, we have to find next three terms. So, we have to find

$5^{th},6^{th}$ and $7^{th}$ terms.

$\Rightarrow$ $5^{th}$ term $=4^{th}$ term + $d=\frac{7}{2}+\frac{1}{2}=\frac{8}{2}=4$

$\Rightarrow$ $6^{th}$ term $=5^{th}$ term + $d=4+\frac{1}{2}=\frac{8+1}{2}=\frac{9}{2}$

$\Rightarrow$ $7^{th}$ term $=6^{th}$ term + $d=\frac{9}{2}+\frac{1}{2}=\frac{10}{2}=5$

Hence, $5^{th},6^{th},$ and $7^{th}$ terms are $4,\frac{9}{2},5$