Math, asked by eminemrules101, 1 year ago

Can someone workout this sum?

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Answers

Answered by NamaBhai

hope it helps.......

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eminemrules101: Cud u explain why....it’s the same formula, right ?

NamaBhai: because a and b are the 1 and 3 terms respectively........

eminemrules101: Ye, so twice the second term will be equal to 1st term + 3rd term...rite ?

NamaBhai: yes....but we have to find a and b.....not a+b

eminemrules101: yes, I’m aware if that...but after finding b in the first step, can’t we substitute in this equation and obtain a?

eminemrules101: Then a will become -1, which is not the answer...how is that possible ?

Answered by varadad25

Question:

Find the value of a, b and c such that a, 7, b, 23 and c are in AP.

Answer:

The required values are a = - 1, b = 15, c = 31.

Step-by-step-explanation:

We have given that,

a, 7, b, 23 and c are in AP.

We know that,

In an AP, the difference between two consecutive terms is constant.

Here,

t₁ = a
t₂ = 7

∴ t₂ - t₁ = 7 - a - - - ( 1 )

Now,

t₃ - t₂ = b - 7 - - - ( 2 )

And,

t₄ - t₃ = 23 - b - - - ( 3 )

As the terms are in AP,

∴ t₃ - t₂ = t₄ - t₃

⇒ b - 7 = 23 - b - - - [ From ( 2 ) & ( 3 ) ]

⇒ b + b = 23 + 7

⇒ 2b = 30

⇒ b = 30 / 2

⇒ b = 15

Now,

t₃ - t₂ = t₂ - t₁

⇒ b - 7 = 7 - a - - - [ From ( 1 ) & ( 2 ) ]

⇒ 15 - 7 = 7 - a

⇒ 8 = 7 - a

⇒ 8 - 7 = - a

⇒ 1 = - a

⇒ a = - 1

Now,

t₅ - t₄ = t₃ - t₂

⇒ c - 23 = b - 7

⇒ c = b - 7 + 23

⇒ c = b + 16

⇒ c = 15 + 16

⇒ c = 31

∴ The required values are a = - 1, b = 15, c = 31.

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