Question

Find 3 consecutive terms which r in AP.whose sum is 24& product is 440

Answer 1

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Heya

Let the three consecutive terms be a + d, a and a - d.

A/q

Sum of these terms = 24

a + d + a + a - d = 24

3a = 24

a = 8

Also,

(a + d)(a)(a - d) = 440

(a + d)(a - d)(a) = 440

Using identity

⏩(x + y)(x - y) = x² - y²⏪

(a² - d²)(a) = 440

Putting the value of a = 8

(8² - d²)(8) = 440

64 - d² = 440/8

64 - d² = 55

d² = 64 - 55

d² = 9

d = √9

d = -3 or +3

Case I :-

When a = 8 and d = -3

a + d = 8 + (-3) = 8 - 3 = 5
a = 8
a - d = 8 - (-3) = 8 + 3 = 11

Case II :-

When a = 8 and d = +3

a + d = 8 + 3 = 11
a = 8
a - d = 8 - (3) = 8 - 3 = 5

Therefore,

The terms are 11, 8 and 5

Hope this helps you.