Question

Example 3. in the following ${AP}_S$ find teh ,missing terms in the boxes :

• A. $2,,26$
• B. $5,,,9\frac{1}{2}$
• C. $,13,,3$
• D. Do all the above options

Answer 1

The correct option is D Do all the above options

Part (A):-

$2,\square ,26$

Then

$a=2$

$a_2=a+d$

$a_3=a+2d$

$a_3=26$

$26=2+2d$

$26-2=2d$

$2d=24$

$d=12$

$Then,$

$a_2=a+d$

$=2+12$

$a_2=14$

Hence, this is the answer.

Part(2):-

$5,\square ,\square ,9\frac{1}{2}$

First term

$a=5$

$a_2=a+d$

$a_3=a+2d$

$a_4=a+3d=9\frac{1}{2}$

$5+3d=\frac{19}{2}$

$3d=\frac{19}{2}-5$

$3d=\frac{19-10}{2}$

$3d=\frac{9}{2}$

$d=\frac{3}{2}$

$Now,$

$a_2=a+d$

$a_2=5+\frac{3}{2}=\frac{13}{2}$

$a_3=a+2d=5+2\times \frac{3}{2}$

$a_3=8$

Hence, this is the answer.

Part (3):-

$a=?$

$a_2=a+d=13......\left(1\right)$

$a_3=a+2d=?$

$a_4=a+3d=3......\left(2\right)$

From equation ()1 and ()2 to and we get,

$a+d=13$

$a+3d=3$

On solving and we get,

$d=4$ put in (1)

$a=9$

Then,

$a_3=a+2d=9+2\times 4=17$

Hence, this is the answer.