Question

If in an A.P, the sum of first 10 terms is 4 times the sum of first five terms, then ratio of
first term and common difference is

Answer 1

Step-by-step explanation:

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Answer 2

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GIVEN:-

sum of first 10terms= 4*(sum of first 5terms)

So, S10=4* S5

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Now,

we know that,

Sn=n/2{2a+(n-1)d}

•°• S10=10/2{2a+(10-1)d}

=>5{2a+9d}

•°• S5=5/2{2a+(5-1)d}

=>5/2{2a+4d}

S10=4*S5 {given}

putting the value of S10 and S5:-

5{2a+9d}=4*5/2{2a+4d}

=>2a+9d=4*1/2{2a+4d}

=>2a+9d=2(2a+4d)

=>2a+9d=4a+8d

=>9d-8d=4a-2a

=>d=2a

=>d/a=2/1

=>a/d=1/2

or,

a:d=1:2

Here, is your answer :)

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