Question

the sum of three numbers in AP is 30 and the product of extreme numbers is 96 the first term of AP is

Answer 1

Answer:

the number are 8,10,12 or 12,10,8

refer to the attachment for the solution

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Answer 2

Answer:

The first term can be  8 or 12

Step-by-step explanation:

Given,

Sum of three numbers in AP is 30

Product of extreme numbers is 96

To find,

The first term of the AP

Solution:

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

Since the sum of three numbers = 30, we have

a+d+a+a-d = 30

3a = 30

a = 10

Product of extreme numbers is 96, we have

(a+d)(a-d) = 96

a² - d² = 96

Substitute the value of 'a' = 10 we get

10² - d² = 96

d² = 100 - 96

d² = 4

d = ±2

If d = 2, the three terms are 8,10,12

If d = -2, the three terms are 12,10,8

∴The first term can be  8 or 12

SPJ2