Question

If the ratio of the sum of two a.p is (7n+1 ):(4n+1) then find the ratio of their 9th term

Answer 1

HERE IS YOUR ANSWER

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Answer 2

ok let's see

AS I AM THE GREATEST

SOLUTION:

TO SOLVE THIS QUESTION WE PUT THE VALUE OF n=2m-1(here m=9)

but why ?

so first I will tell you how to solve .( the prove)

WE HAVE GIVEN SUM OF n terms ratio

which is

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

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

SO WE HAVE

=2a+(n-1)d/2a'+(n-1)d'......eq1

now the ratio of mth terms

=a+(m-1)d/a'+(m-1)d'

multiply it by 2/2

we get

=2a+2(m-1)d/2a'+(m-1)d'..eq2.

now we will compare

eq1 with eq2

we see that in numerator and denominator

first term is same and common difference is same just the difference is in middle term which in eq1 is (n-1) and in eq2 is 2(m-1)

so to find the ratio of the mth terms from sum of nth terms

we will equate them

we get

n-1=2m-2

so n=2m-1..eq3

Now we come to the question

as we get relation from eq3

in this question we have to find 9th terms ratio

from the ratio given ratio (7n+1)/(4n+1)

from eq3 we get

n=2×9-1

n=17

Then ratio of mth terms

=7×17+1/4×17+1

=120/69

=40/23

the ratio is 40:23

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