Question

Sum of three consecutive term of an arithmetic progression is 42 and their product is 2520. Find the term of arithmetic progression

Answer 1

Answer :

10 , 14 , 18 or 18 , 14 , 10 are terms of the Arithmetic Progression if Sum of three consecutive terms of an Arithmetic Progression is 42 and their product is 2520.

Step-by-step explanation:

Let say three terms of an AP are

a - d , a , a + d

Sum = a - d + a + a + d = 3a

3a = 42

=> a = 14

(a - d)a (a + d) = 2520

=> (14 - d)14(14 + d) = 2520

=> 196 - d² = 180

=> d² = 16

=> d = ± 4

Three terms are 10 , 14 , 18 or 18 , 14 , 10

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Answer 2

GIVEN :

Sum of three consecutive terms in an Arithmetic Progression = 42

Their product = 2520

Let the terms be (a - d), a and (a + d)

(a - d) + a + a + d = 42

a - d + a + a + d = 42

=> 3a = 42

=> a = 42/3

=> a = 14

(a - d) × a × (a + d)

(a - d) × 14 × (a + d) = 2520

(a - d) (a + d) = 2520/14

a² - d² = 180 [ (a - b) (a + b) = a² - b² ]

(14)² - d² = 180

196 - 180 = d²

=> d² = 16

=> d = √16

=> d = ±4

TERMS :

If d = -4,

First term = a - d = 14 - (-4) = 18

Second term = a = 14

Third term = a + d = 14 + (-4) = 10

If d = 4,

First term = a - d = 14 - 4 = 10

Second term = a = 14

Third term = a + d = 14 + 4 = 18

Therefore, the terms are 18, 14 and 10 or 10, 14 and 18.

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