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Easy

Question

If the ratio of the sum to $n$ terms of two A.P.’s is $open parentheses 5 n plus 3 close parentheses colon left parenthesis 3 n plus 4 right parenthesis$ , then the ratio of their 17^th terms is

172:99
168:103
175:99
171:103

The correct answer is: 168:103

$fraction numerator fraction numerator n over denominator 2 end fraction left parenthesis 2 a plus left parenthesis n minus 1 right parenthesis d right parenthesis over denominator fraction numerator n over denominator 2 end fraction left parenthesis 2 a to the power of ´ end exponent plus open parentheses n minus 1 close parentheses d to the power of ´ end exponent right parenthesis end fraction equals fraction numerator 5 n plus 3 over denominator 3 n plus 4 end fraction$
$rightwards double arrow blank fraction numerator left parenthesis 2 a plus left parenthesis 2 n minus 2 right parenthesis d right parenthesis over denominator left parenthesis 2 a to the power of ´ end exponent plus open parentheses 2 n minus 2 close parentheses d to the power of ´ end exponent right parenthesis end fraction equals fraction numerator 5 open parentheses 2 n minus 1 close parentheses plus 3 over denominator 3 open parentheses 2 n minus 1 close parentheses plus 4 end fraction blank left parenthesis r e p l a c e blank n blank b y blank 2 n minus 1 right parenthesis$
$rightwards double arrow blank fraction numerator left parenthesis a plus left parenthesis n minus 1 right parenthesis d right parenthesis over denominator left parenthesis a to the power of ´ end exponent plus open parentheses n minus 1 close parentheses d to the power of ´ end exponent right parenthesis end fraction equals fraction numerator 10 n minus 2 over denominator 6 n plus 1 end fraction$
$rightwards double arrow blank fraction numerator left parenthesis a plus left parenthesis 17 minus 1 right parenthesis d right parenthesis over denominator left parenthesis a to the power of ´ end exponent plus open parentheses 17 minus 1 close parentheses d to the power of ´ end exponent right parenthesis end fraction equals fraction numerator 168 over denominator 103 end fraction$

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