The second and fifth term of a geometric series are 750 and -6 respectively. Find the common ratio of and the first term of the series?

1 Answer
Mar 1, 2017

Answer:

#r=-1/5,a_1=-3750#

Explanation:

The #color(blue)"nth term of a geometric sequence"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(a_n=ar^(n-1))color(white)(2/2)|)))#
where a is the first term and r, the common ratio.

#rArr"second term "=ar^1=750to(1)#

#rArr"fifth term "=ar^4=-6to(2)#

To find r, divide ( 2) by ( 1)

#rArr(cancel(a)r^4)/(cancel(a)r)=(-6)/750#

#rArrr^3=-1/125rArrr=-1/5#

Substitute this value into ( 1) to find a

#rArraxx-1/5=750#

#rArra=750/(-1/5)=-3750#