Question

For the AP ($\frac{3}{2}$ ),($\frac{1}{2}$ ),(-$\frac{1}{2}$ ),(-$\frac{3}{2}$ ),… write the first term a and the common difference d. Also write the next two terms after the given last term -$\frac{3}{2}$

Answer 1

We have , $a_1$ = $\frac{3}{2}$ , $a_2$ = $\frac{1}{2}$ , $a_3$ = - $\frac{1}{2}$ , $a_4$ = - $\frac{3}{2}$

Thus a = $\frac{3}{2}$

$a_2$ - $a_1$ = ($\frac{1}{2}$) - ($\frac{3}{2}$) = -1

$a_3$ - $a_2$ = (-$\frac{1}{2}$) - ($\frac{1}{2}$) = -1 ,

$a_4$ - $a_3$ = (-$\frac{1}{2}$) - ( - $\frac{1}{2}$) = 1 , and so on

$\Rightarrow$ d = -1

Now , we find the successor of - ( - $\frac{3}{2}$)

$a_5$ = ( - $\frac{3}{2}$) + d = ( - $\frac{3}{2}$) + (-1) = ( - $\frac{5}{2}$)

Then $a_6$ = $a_5$ + d = ( - $\frac{5}{2}$) + (-1) = - $\frac{7}{2}$

Hence , the next two terms after given terms ( - $\frac{3}{2}$) are ( - $\frac{5}{2}$) and ( - $\frac{7}{2}$)