What is the fifteenth term of the sequence 5,-10,20,-40,80?

1 Answer

Answer:

#a_15=81920#

Explanation:

from the given set of numbers 5,-10,20,-40,80...it appears like Geometric Sequence and with first term #a_1=5# and the common ratio #r=80/(-40)=(-40)/20=20/(-10)=(-10)/5=-2#

#r=-2#

the formula to find the #nth# term in Geometric Progression is

#a_n=a_1*r^(n-1)#

Use now #a_1=5# and #r=-2# and #n=15# in the formula

#a_n=a_1*r^(n-1)#

#a_15=5*(-2)^(15-1)#

#a_15=5*(-2)^(14)#

#a_15=5*16384#

#a_15=81920" " "#the 15th term

A long check helps after all there are only 15 numbers

5, -10, 20, -40, 80, -160, 320, -640, 1280, -2560, 5120, -10240, 20480, -40960, 81920

God bless....I hope the explanation is useful...