Question

the ratio of 7th to the 3rd term of an AP is 12:5 find the ratio of 13th to the 4th term ​

Answer 1

Answer:

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Answer 2

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Answer :

$a_{13}:a_4=10:3$

Step-by-step explanation :

Given ,

$a_{7}:a_{3}=12:5\\\\=>\frac{a_7}{a_3}=\frac{12}{5}\\\\ =>\frac{a+6d}{a+2d}=\frac{12}{5}\\\\ =>5a+30d=12a+24d\\\\=>7a=6d\\\\=>a=\frac{6d}{7}$

$Now,\frac{a_{13}}{a_{4}}=\frac{a+12d}{a+3d}\\\\ =>\frac{\frac{6d}{7} +12d}{\frac{6d}{7}+3d}\\\\ =>\frac{6d+84d}{6d+21d}\\\\ =>\frac{90d}{27d}\\\\ =>\frac{30}{9}\\\\ =>\frac{10}{3}$

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