Question

2.
(a) The sum of three terms of an A.P. is 21 and their product is 336. Find the numbers.

Answer 1

consider three numbers of AP is x, 2 x, 3x.

1st condition.

x × 2x × 3x = 336

Answer 2

Answer:

Let the first term be "a-d" and common difference be "d"

Therefore the terms are :_ a-d , a , a+d .

A/Qn

a-d + a + a+d = 21

3a = 21 [ since " d - d = 0 " ]

Therefore :_ a = 7 [ since " 21/3 = " 7 ]

Again

( a - d ) * a * ( a + d ) = 336

( a - d ) * ( a + d ) = 336/a

a^2 - d^2 = 336/a

7^2 - d^2 = 336/7 [ since " a = 7 " ]

49 - d^2 = 48

d^2 = 49 - 48

d^2 = 1

d = √1

d = 1

Therefore :_ The terms are

a - d = 7 - 1 = 6 [ since a = 7 and d = 1 ]

a = 7

and a + d = 7 + 1 = 8

Now sum of 6 + 7 + 8 = 21

and 6 * 7 * 8 = 336