Question

The sum of 3 numbers in A.P is 15 and sum of squares of the extreme terms is 58.Find the numbers.

Answer 1

Hi ,

Let ( a - d ) , a , ( a + d ) are three numbers in

A.P

1 ) a - d + a + a + d = 15 ( given )

3a = 15

a = 15/3

a = 5

2 ) Sum of the extremes = 58

( a - d )² + ( a + d )² = 58

2( a² + d² ) = 58

a² + d² = 29

5² + d² = 29 [ since a = 5 ]

d² = 29 - 25

d² = 4

d = ± 2

Therefore ,

Required numbers are

If a = 5 , d = 2

i ) a - d = 5 - 2 = 3

a = 5 ,

a + d = 5 + 2 = 7

3 , 5 , 7

ii ) If a = 5 , d = -2

required numbers are ,

3 , 5 , 7

I hope this helps you.

: )

Answer 2

Answer:

The required A.P or numbers are 3,5,7 or 7,5,3.      

Step-by-step explanation:

Given : The sum of 3 numbers in A.P is 15 and sum of squares of the extreme terms is 58.

To find : The numbers?

Solution :

Let The terms in A.P is a-d, a ,a+d.

According to question,

The sum of 3 numbers in A.P is 15.

i.e. $a-d+a+a+d=15$

$3a=15$

$a=\frac{15}{3}$

$a=5$

The sum of squares of the extreme terms is 58.

$(a-d)^2+(a+d)^2= 58$

$a^2+d^2-2ad+a^2+d^2+2ad= 58$

$2(a^2+d^2)= 58$

$a^2+d^2= 29$

Substitute a=5,

$5^2+d^2= 29$

$25+d^2= 29$

$d^2=29-25$

$d^2=4$

$d=\sqrt{4}$

$d=2,-2$

Now, When a=5 and d=2 the AP is

a-d=5-2=3

a=5

a+d=5+2=7

The required A.P or numbers are 3,5,7.

Now, When a=5 and d=-2 the AP is

a-d=5+2=7

a=5

a+d=5-2=3

The required A.P or numbers are 7,5,3.