Question

In an AP sum of first 3 terms is 21 & product is 231 find the 3 terms of an AP.

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Answer 1

I hope this answer will help you

Answer 2

Answer:

3, 7, 11

Step-by-step explanation:

⇒ Let the three terms be a, a + d and a + 2d.

⇒ Sum of the terms = 21,

$\bullet\ a+a+d+a+2d=21 \\ \\ \bullet\ 3a+3d=21 \\ \\ \bullet\ 3(a+d)=21 \\ \\ \bullet\ a+d=7$

⇒ Thus second term is 7.

⇒ So, a = a + d - d = 7 - d &  a + 2d = a + d + d = 7 + d.

⇒ Product of terms = 231,

$\bullet\ a(a+d)(a+2d)=231 \\ \\ \bullet\ (7-d) \ 7 \ (7+d)=231 \\ \\ \bullet\ 7(7-d)(7+d)=231 \\ \\ \bullet\ 7(49-d^2)=231 \\ \\ \bullet\ 49-d^2=33 \\ \\ \bullet\ d^2=49-33 \\ \\ \bullet\ d^2=16 \\ \\ \bullet\ d=\pm 4$

⇒ Thus the common difference is either 4 or -4.

⇒ By considering d = 4,

• a = 7 - d = 7 - 4 = 3
• a + 2d = 7 + d = 7 + 4 = 11

⇒ By considering d = -4,

• a = 7 - d = 7 - (-4) = 7 + 4 = 11
• a + 2d = 7 + d = 7 + (-4) = 7 - 4 = 3

⇒ Thus the three terms are 3, 7 and 11.