Math, asked by anjali242003, 1 year ago

The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last term to the product of two middle terms is 7:15. Find the numbers

Answers

Answered by Narendra931

more detail contect 8890085771

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Narendra931: because if you assume these than you can solv easely

nitthesh7: as I've said to make the problem simpler we take both positive and negative signs to cancel the d values easily = (a-3d)+(a-d)+(a+d)+(a+3d) = 32

anjali242003: I can solve easily but how would I know I have to take these terms??

anjali242003: And why 3d why not 2d

Narendra931: because you take 2d then difference not common

nitthesh7: And why 3d why not 2d = bcoz the common difference would change as it goes +1 and +2 which is impossible

anjali242003: Ooo ok thank u both

nitthesh7: NM all the best for ur xams

anjali242003: Thank u

nitthesh7: NM

Answered by nitthesh7

Let the no/s be of the form (a-3d) (a-d) (a+d) (a+2d)

Then according to question,

(a-3d)+(a-d)+(a+d)+(a+3d) = 32

4a = 32

a = 8

Also,

$\frac{(a-3d)(a+3d)}{(a-d)(a+d)}$ = $\frac{7}{15}$

15(a²-9d²) = 7(a²-d²)

15a² - 135d² = 7a² - 7d²

8a² - 128d² = 0

⇒Divide by 8 on whole

⇒ a² - 16d²

⇒Substituting a =8, Then

⇒ 8² - 16d²

⇒64 - 16d²

⇒(8+4d)(8-4d)

Then d = +2, -2
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If d = +2 , Then

No/s - (2, 6, 10, 14)
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If d = -2 , Then

No/s - (14,10, 6, 2)
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Hence the no/s would be (2, 6, 10, 14) or (14, 10, 6, 2)

☺☺☺ Hope this Helps ☺☺☺

nitthesh7: If u find it as most helpful pls mark it as brainliest

nitthesh7: TQ for Brainliest

anjali242003: Wc

nitthesh7: ☺☺☺

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