###
**If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is :**

A. 13
B. 9
C. 21
D. 17**Answer: Option C**

## Show Answer

Solution(By Apex Team)

Let three consecutive terms of an increasing A.P. be a – d, a + d
where a is the first term and d be the common difference
$\begin{aligned}&\therefore a-d+a+a+d=51\\
&\Rightarrow3a+51\\
&\therefore a=\frac{51}{3}=17\end{aligned}$
and product of the first and third terms
$\begin{array}{l}=(a-d)(a+d)=273\\
\Rightarrow a^2-d^2=273\\
\Rightarrow(17)^2-d^2=273\\
\Rightarrow289-d^2=273\\
\Rightarrow d^2=289-273\\
\Rightarrow d^2=16\\
\Rightarrow d^2=(\pm4)^2\\
\therefore d=\pm4\\
\because\text{ The A.P. is increasing }\\
\therefore d=4\\
\text{ Now third term }=a+d\\
=17+4=21\end{array}$

## Related Questions On Progressions

### How many terms are there in 20, 25, 30 . . . . . . 140?

A. 22B. 25

C. 23

D. 24

### Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.

A. 5B. 6

C. 4

D. 3

### Find the 15th term of the sequence 20, 15, 10 . . .

A. -45B. -55

C. -50

D. 0

### The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is

A. 600B. 765

C. 640

D. 680