Question

The sum of first three terms in an
AP is 18 or if the product of first and the third term is 5 times the common diffrence find three numbers​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

$\bf{\Huge{\underline{\boxed{\rm{\red{ANSWER\::}}}}}}$

Given:

The sum of first three terms in an A.P. is 18 or if the product of first and the third is 5 times the common difference.

To find:

The three numbers of A.P.

$\large{\underline{\text{Explanation\::}}}$

General Terms of Arithmetic Progression:

Let a be the first term and d be the common difference of an A.P.

Let the three terms of numbers be;

• First term= a-d
• Second term= a
• Third term= a+d

A/q,

→ a-d + a + a+d = 18

→ 3a = 18

→ a = $\cancel{\frac{18}{3} }$

→ a = 6

∴The product of first term and third term is 5 times the common difference;

→ (a-d)(a+d) = 5d

→ a² - d² = 5d

→ (6)² - d² = 5d        [∴ a= 6]

→ 36 - d² = 5d

→ d² + 5d -36 =0

[Factorization]

→ d² +9d -4d -36 = 0

→ d(d+9) -4(d+9)= 0

→ (d+9)(d-4) = 0

→ d+9= 0  or   d-4 = 0

→ d = -9  or  d= 4

For d = -9;

• First term= 6 -(-9) = 6+9= 15
• Second term= 6
• Third term= 6+(-9)= 6-9= -3

For d = 4;

• First term= 6-4= 2
• Second term= 6
• Third term= 6+4= 10