Question 551098: Find the tenth term of the sequence 5,-25, 125, -625,...
Answer by mathstutor458(57)   (Show Source):
You can put this solution on YOUR website! the sequence 5,-25, 125, -625,...
first number = 5
second number = 5 * (-5) =-25
third number = -25 * (-5) = 125
fourth number = 125 * (-5) = -625
which means, next number in series = previous number in series * (-5)
Therefore,
5th number = -625 * (-5)
6th number = (5th number) * (-5) = -625 * (-5) *(-5) = -625 * 25
like wise,
7th number = -625 * 25 * (-5) = -625 * -125
8th number = -625 * -125 * (-5) = -625 * 625
9th number = -625 * 625 * (-5)
10th number = -625 * 625 * -5 * (-5) = -625 *625 *25= -9765625 --->answer
(or)
another method:-
the sequence 5,-25, 125, -625,... is in geometric series
first term a1= 5
common ratio r= -25/5 = -5
nth term = a1*r^(n-1)
10th term = 5 *(-5)^(10-1)
= 5 * (-5)^9 = -9765625
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