Question

Question 1 Find the 20th and nthterms of the G.P. 5/2, 5/4, 5/8,...

Class X1 - Maths -Sequences and Series Page 192

Answer 1

$The\: series\:are:\frac{5}{2},\frac{5}{2^2},\frac{5}{2^3},.......are\:in\:GP\\\\here,a=\frac{5}{2},and\:r=\frac{\frac{5}{2^2}}{\frac{5}{2}}=\frac{1}{2}\\\\T_n=ar^{n-1}\\T_{20}=ar^{20-1}\\=\frac{5}{2}{(\frac{1}{2})}^{n-1}\\=\frac{5}{2^{20}}\\\\\\again,\\T_n=\frac{5}{2}\times{(\frac{1}{2})}^{n-1}\\\\=\frac{5}{2}\times\frac{1}{2^{n-1}}\\\\=\frac{5}{2^n}$