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

Answer 1

(ii)
$2,\frac{5}{2},3,\frac{7}{2}\dots \dots Here,a_2-a_1=\frac{5}{2}-2=\frac{1}{2}{a}_3-a_2=3-\frac{5}{2}=\frac{1}{2}{a}_4-a_3=\frac{7}{2}-3=\frac{1}{2}\Rightarrow a_{n+1}-a_{n}issameforalln.Therefore,d=\frac{1}{2}andthegivennumbersareinA.P.Nextthreetermsare:a_5=\frac{7}{2}+\frac{1}{2}=4a_6=4+\frac{1}{2}=\frac{9}{2}{a}_7=\frac{9}{2}+\frac{1}{2}=5$