Question

Check if the series is an A.P. Find the common difference $d$ and write three more terms of the the following series.

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

• A. $a=2$; $d=\frac{1}{2}$; other terms $4,$ $\frac{9}{2},5$
• B. $a=3$; $d=\frac{1}{2}$; other terms $6,8,10$
• C. $a=2$; $d=\frac{3}{2}$; other terms $7,8,15$
• D. $a=3$; $d=\frac{3}{2}$; other terms $4,5,15$

Answer 1

The correct option is A $a=2$; $d=\frac{1}{2}$; other terms $4,$ $\frac{9}{2},5$

It is an A.P. because $a=2$, $d=\frac{1}{2}$
$\because \left[\right(t_2-t_1)=(t_3-t_2)=(t_4-t_3)=\frac{1}{2}]$
$t_5=\frac{7}{2}+\frac{1}{2}=4$
$t_6=4+\frac{1}{2}=\frac{9}{2}$
$t_7=\frac{9}{2}+\frac{1}{2}=5$