Question

Question 4 (ii)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(ii) $2,\frac{5}{2},3,\frac{7}{2},\dots$

Answer 1

If the difference between any two consecutive terms of a series is a constant value, then the series is an A.P

Given, the series is :
$2,\frac{5}{2},3,\frac{7}{2}\dots$
Here,
$a_2-a_1=\frac{5}{2}-2=\frac{1}{2}{a}_3-a_2=3-\frac{5}{2}=\frac{1}{2}{a}_4-a_3=\frac{7}{2}-3=\frac{1}{2}$

Note that the difference between any two consecutive terms of the series is a constant value.
Therefore, $d=\frac{1}{2}$ and the given numbers are in A.P.
The next three terms are:
$a_5=\frac{7}{2}+\frac{1}{2}=4a_6=4+\frac{1}{2}=\frac{9}{2}{a}_7=\frac{9}{2}+\frac{1}{2}=5$