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# Which of the following are APs? If they form an AP, find the common difference $d$ and write three more terms.

$2, \frac{5}{2}, 3, \frac{7}{2}, â€¦â€¦.$

Given:

Given sequence is $2, \frac{5}{2}, 3, \frac{7}{2}, …….$

To do:

We have to check whether the given sequence is an AP. If it is an AP we have to find the common difference $d$ and write three more terms.

Solution:

In the given sequence,

$a_1=2, a_2=\frac{5}{2}, a_3=3$

$a_2-a_1=\frac{5}{2}-2=\frac{5-4}{2}=\frac{1}{2}$

$a_3-a_2=3-\frac{5}{2}=\frac{6-5}{2}=\frac{1}{2}$

$a_2 - a_1 = a_3 - a_2$

$d=a_2 - a_1=\frac{1}{2}$

$a_5=a_4+d=\frac{7}{2}+\frac{1}{2}=\frac{7+1}{2}=\frac{8}{2}=4$

$a_6=a_5+d=4+\frac{1}{2}=\frac{8+1}{2}=\frac{9}{2}$

$a_7=a_6+d=\frac{9}{2}+\frac{1}{2}=\frac{9+1}{2}=\frac{10}{2}=5$

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