Question

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 1

Answer:

The third term is 21.

Among the given options option (c) 21 is correct.  

Step-by-step explanation:

Let the 3 consecutive terms of an A.P is (a - d) , a, (a + d)  

Given :  

Sum of 3 consecutive terms is 51.

(a - d) + a + (a + d) = 51

3a - d + d = 51

3a = 51

a = 51/3

a = 17

Product of first and third terms = 273 (Given)

(a - d) (a + d) = 273

a² - d² = 273

17² - d² = 273

289 - d² = 273

d² = 289 - 273

d² = 16

d = √16

d = 4

Third term = a + d  

a3 = 17 + 4  

a3  = 21

Hence, the third term is 21.

HOPE THIS ANSWER WILL HELP YOU….

 

Answer 2

Given:

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.

To find:

third term i.e. A3

Solution:

Let the 3 consecutive terms of an A.P is A1 = (a - d)

A2 = a

A3 = (a + d)

ATQ:

A1 + A2 + A3 = 51

(a - d) + a + (a + d) = 51

3a - d + d = 51

3a = 51

a = 51/3

a = 17

and

A1 × A2 = 273

(a - d) (a + d) = 273

a² - d² = 273

17² - d² = 273

289 - d² = 273

d² = 289 - 273

d² = 16

d = √16

d = 4

Now,

3rd term = a + d

a3 = 17 + 4

a3 = 21

option: c) 21