Question

19. Find three numbers in A.P., whose sum is 15 and the product is 80.
Hint: Let the required numbers be (a - d), a, (a + d).]
AP Whose common difference is 10°. Find the​

Answer 1

Answer:

let a − d, a, a +d are three terms of

Here, sum of the terms = 15

Or, a − d + a + a + d = 15

Or, 3a = 15

Or, a = 15/3

Or, a = 5

Also, product = 80

(a − d)a(a + d) = 80

(a² − d²)a = 80

(5² − d²)5 = 80

25 − d² = 80/5

25 − d² = 16

−d² = −9

d² = 3²

d = ±3

Therefore, a = 5, d = ±3

required 3 terms are

a − d = 5 − 3 = 2

a = 5

a + d = 5 + 3 = 8

(2, 5, 8) or (8, 5, 2)

Answer 2

Answer:-

The three terms are:

[2 , 5 , 8 ]

or

[ 8 , 5 , 2 ]

• Given:-

Sum of three numbers in A.P = 15

Product of three numbers in A.P = 80

• To Find:-

The three numbers = ?

• Solution:-

Let the three terms of A.P be a - d , a , a + d

ATQ:-

→ a - d + a + a + d = 15

→ 3a = 15

→ a = $\dfrac{15}{3}$

→ a = 5

Also,

→ ( a - d ) × a × ( a + d ) = 80

→ ( a² - d² ) a = 80

• Substituting the value of a here,

→ ( 5² - d² ) 5 = 80

→ 25 - d² = $\dfrac{80}{5}$

→ 25 - d² = 16

→ d² = 9

→ d² = (3)²

→ d = ± 3

Therefore,

$\boxed{a = 5}$

$\boxed{d = \pm 3}$

Hence, the 3 terms are,

→ a - d = 5 - 3 = 2

$\pink{\bigstar}$ 2

→ a = 5

$\pink{\bigstar}$ 5

→ a+ d = 5 + 3 = 8

$\pink{\bigstar}$ 8

$\red{\bigstar}$ HENCE,

[2 , 5 , 8 ]

or

[ 8 , 5 , 2 ]