Question 1

Find the 20th and nthterms of the G.P. $5 over 2 comma 5 over 4 comma 5 over 8 comma...$

Answer

Here, a = First Term = $5 over 2$

r = common ratio = $fraction numerator begin display style 5 over 4 end style over denominator begin display style 5 over 2 end style end fraction equals 1 half$

$a subscript 20 space space end subscript equals space a r to the power of 20 minus 1 end exponent equals 5 over 2 open parentheses 1 half close parentheses to the power of 19 equals fraction numerator 5 over denominator open parentheses 2 close parentheses open parentheses 2 close parentheses to the power of 19 end fraction equals 5 over open parentheses 2 close parentheses to the power of 20 a subscript n space equals space a r to the power of n minus 1 end exponent equals 5 over 2 open parentheses 1 half close parentheses to the power of n minus 1 end exponent equals fraction numerator 5 over denominator open parentheses 2 close parentheses open parentheses 2 close parentheses to the power of n minus 1 end exponent end fraction equals 5 over open parentheses 2 close parentheses to the power of n$