Question

The sum of first three terms of an AP is 24and the sum of their squares is 224.Find the first three terms of the AP.

Answer 1

Answer:

4 , 8 and 12 are the numbers .

Step-by-step explanation:

Let the A.P be a - d , a , a + d .

Here d = common difference .

Note that the sum of first 3 numbers = 24 .

1 st number = a - d

2 nd number = a

3 rd number = a + d

a - d + a + a + d = 24

⇒ 3 a = 24

⇒ a = 24/3

⇒ a = 8

So a = 8 .

Now sum of squares = 224 .

⇒ ( a - d )² + a² + ( a + d )² = 224

⇒ a² + d² - 2 ad + a² + a² + 2 ad + d² = 224

⇒ 3 a² + 2 d² = 224

⇒ 3 ( 8 )² + 2 d² = 224

⇒ 3 × 64 + 2 d² = 224

⇒ 192 + 2 d² = 224

⇒ 2 d² = 224 - 192

⇒ d² = 32 / 2

⇒ d² = 16

⇒ d = ± 4

So a - d , a , a + d

= 8 - 4 , 8 , 8 + 4

= 4 , 8 , 12

or , a - d , a , a + d

= 8 + 4 , 8 , 8 - 4,

= 12 , 8 , 4 .

NOTE :

The formula used for ( a - b )² = a² + b² - 2 ab

The formula used for ( a + b )² = a² + b² + 2 ab

When we are comparing a² = x

Then note that a = ± √x