Question

sum of the product of 3 terms in ap are 15 and 105 respectively. find the 3 terms​

Answer 1

Answer:

The three numbers in ap whose product is 105. = 7, 5 and 3. Hope it helps

Step-by-step explanation:

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Answer 2

A N S W E R :

Let's consider that three term of AP be a, (a + d), (a – d) respectively.

By CONDITION :

❭❭ Sum of three terms of AP is 15.

⇥a + a + d + a – d = 15

⇥ 3a = 15

⇥ a = 15/3

⇥ a = 5⠀⠀⠀⠀⠀⠀⠀⠀⠀ —eq.( I )

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀

❭❭ Product of three terms of AP is 105.

⠀⠀⠀

➟ a × (a + d) × (a – d) = 105

➟ a(a² – d²) = 105

➟ 5(5² – d²) = 105⠀⠀⠀⠀⠀⠀[From eq. ( I )]

➟ 25 – d² = 105/5

➟ 25 – d² = 21

➟ – d² = 21 – 25

➟ – d² = – 4

➟ d = √4

➟ d = ±2

⠀⠀⠀

Therefore,

⠀⠀⠀

• First term, a = 5.
• Second term, (a + d) = (5 + 2) = 7.
• Third term, (a – d) = (5 – 2) = 3.

⠀⠀⠀

∴ Hence, the required three terms are 5, 7 and 3 respectively$.$