Question

Please send your solution (with steps)
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Answer 1

Answer:

32n+54

Step-by-step explanation:

(7nx4n)+(7nx27) +(1x4n) +(1x27)

(28n+4n)+(27+27)

32n+54

Answer 2

Answer:

am₁ : am₂ = P = 14m-6:8m+223

Step-by-step explanation:

Given:- if the ratio of first n term of two A.P.S is (7n+1 ): (4n+27)

Find :- The ratio of their mth term .

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Let a₁ , a₂ and d₁ d₂ be the first term and common difference of two A. P. S

Sn₁ = n/2{2a₁ +(n-1)d₁ }

Sn₂ = n/2( 2a₂ + (n-1)d₂}

But , sn₁ /sn₂ = 7n+1/4n+27

∴ 2a₁ + (n-1)d₁ /2a₂ + (n-1)d₂ = 7n+1/4n+27 _____(1)

As we know that , to find nth term

it's standard formula is a+(n-1)d

So dividing by 2 in eq(1)'s numerator and denomenator .

We get , a₁ + (n-1)/2*d₁ /a₂+(n-1)/2*d₂ = 7n+1/4n+27 _____(2)

Now, We have to find mth term of each APS

am₁ = a₁+ (m ₁-1)d₁

am₁ = a₁+ (m ₁-1)d₁ am₂ = a₂ + (m₂-1)d₂

Comparing am₁ to a₁+(n-1)/2 *d₁

we get , n-1/2= m-1

n = 2m-1

Now putting n = 2m -1

⟹ a₁ +(m-1)d₁ /a₂ + (m-1)d₂ = 7(2m-1)+1/4(2m-1) +27 = 14m-6/8m+23

∴am₁ /am₂ = 14m-6/8m+23

So ,P = 14m-6/8m+23 Answer..