Question

If the Sum and product of 3 consecutive terms
of an A.P. are 12 and 48 respectively then the terms
​

Answer 1

Step-by-step explanation:

• Ans is in image ..........

Answer 2

$\large\bf\underline{Given:-}$

• Sum of three consecutive terms of AP = 12
• Product of three consecutive terms = 48

$\large\bf\underline {To \: find:-}$

• Consecutive terms

$\huge\bf\underline{Solution:-}$

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

Sum of 3 consecutive terms = 12

➙ (a - d) + a + (a + d ) = 12

➙ a + a + a - d + d = 12

➙ 3a = 12

➙ a = 12/3

• ➙ a = 4

Product of 3 consecutive terms = 48

➙ (a - d) × a × (a + d) = 48

we know that

• ≫ (a + b)(a - b) = a² - b², then

➙ (a² - d²) × a = 48

• putting value of a = 4

➙ (4² - d²) × 4 = 48

➙ 16 - d² = 48/4

➙ 16 - d² = 12

➙ -d² = 12 - 16

➙ - d² = -4

➙ d = √4

• ➙ d = 2

So,

three consecutive terms are :-

• (a - d) = 4 -2 = 2
• a = 4
• (a + d) = 4 + 2 = 6

three consecutive terms ,when d = -2 :-

• (a - d) = 4 -(-2) = 6
• a = 4
• (a + d) = 4 - 2 = 2

Hence,

3 consecutive terms when d = 2 are :-

• ≫ 2 , 4 ,6

3 consecutive terms when d = -2 are :-

• ≫ 6, 4 , 2

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