Find the 9 th term and the general term of the progression 1 4 , ? - 1 2 , ? 1 , ? - 2 , ? …

Question

Find the $9^{th}$ term and the general term of the progression $\frac{1}{4}, - \frac{1}{2}, 1, - 2, \dots$

Smart Achievers · Accepted Answer

(1)

$The given progression is clearly a G.P. with first term$ $\frac{1}{4}, - \frac{1}{2}, 1, - 2, \dots$

$∴$ $9^{th} term = a_{9} = a r^{8} = \frac{1}{4} {(- 2)}^{8} = 64$

$and general term = a_{n} = a r^{n - 1} = \frac{1}{4} {(- 2)}^{n - 1} = {(- 1)}^{n - 1} 2^{n - 3}$

Want Us to Email you About Special Offers & Updates?