Question

if three numbers are in A.P . the sum of these number is 27 and sum of their squres is 275 then find the a.p's terms​

Answer 1

Step-by-step explanation:

The required AP is 4, 9, 14, 19,....

Step-by-step explanation:

Let the three numbers are (a-d), a, a+d.

The sum of three numbers in AP is 27.

The sum of those three numbers squares is 293.

(a=9)

The common difference is 5. The AP is defined as

Therefore the required AP is 4, 9, 14, 19,....

Answer 2

$\bigstar$ EXPLAINATION $\bigstar$

• Given

Sum of three numbers which are in AP = 27

Sum of their squares of the three numbers = 275

• How to find

Whenever they give three numbers are in AP then consider the three numbers as a - d, a, a + d

Then apply AP condition and slove the equations

• Procedure

Let the three numbers be a - d, a, a + d

a - d, a, a + d are in AP

Given,

Sum of the three terms = 27

But the sum of the three terms = (a - d) + a + (a + d) = 3a

$3a = 27 \\ a = 27/3$

$a = 9$

Given,

Sum of their squares = 275

But the sum of their squares = (a - d)² + a² + (a + d)² = a² + d² - 2ad + a² + a² + d² + 2ad = 2(a² + d²)

We know that,

a = 9

Therefore,

Sum of their squares = 2(81 + d²) = 162 + 2d²

$162 + 2d² = 275$

$2d² = 275 - 162 = 113$

${d}^{2} = \frac{113}{2} = 56.5$

$d = \sqrt{56.5}$

$d = 7.516$

• Extra Information

$Tn\:of\:AP = a + (n - 1)d$

$Sn\:of\:AP = \frac{n}{2} \times [2a + (n-1)d]$

$Sn\:of\:AP = \frac{n}{2} \times (a + l)$

$Tn\:of\:GP = a \times r^(n-1)$

$Sn\:of\:GP = \frac{a(r^n - 1)}{(r-1)}$