Question

If the ratio of the sum of the first n terms of two A.Ps is (7n+1):(4n+27) , then find the ratio of their 9th terms.

Answer 1

Arithmetic progression. AP.

To find ratio of 9th terms given ratio of sum of n terms.

$S1_n=\frac{n}{2}[2a_1+(n-1)d_1]\\S2_n=\frac{n}{2}[2a_2+(n-1)d_2]\\\\\frac{S1_n}{S2_n}=\frac{2a_1+(n-1)d_1}{2a_2+(n-1)d_2}=\frac{7n+1}{4n+27}=\frac{8+(n-1)7}{31+(n-1)4}\\\\So \: \: a_1=4k, \: a_2=31 k, \: \: d_1=7k, \: \: d_2=4k, \ \ for \: some \: k.\\\\LHS=\frac{T1_9}{T2_9}=\frac{a_1+8d_1}{a_2+8d_2}=\frac{4k+8*7k}{31k+8*4k}\\\\=\frac{20}{21}$

Answer is 20/21.

Answer 2

Hey mate..
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Please see the given pic attentively to figure the solution out.

#racks