How do you find the 7th term in the geometric sequence 2, 6, 18, 54, ...?

1 Answer
KillerBunny
Nov 10, 2015

#4374#

Explanation:

In a geometric sequence, you choose a first term #a#, a ratio #r#, and then you obtain every term multiplying the previous one by the ratio. Let's compute some terms:

  • #a_0 = a#
  • #a_1 = a*r#
  • #a_2 = (a*r)r = a*r^2#
  • #a_3 = (a*r^2)r = a*r^3#

and so on. We can see that the relation is #a_n = a*r^n#, which means that the seventh term is #a_7=a*r^7#.

In your case, the first term #a# is #2#, and the ratio can be easily computed: if #a_0=2# and #a_1=6#, then #a_1=a_0*r=6#, which means #2*r=6#, and finally #r=3#.

So, the seventh term will be #2*3^7 = 2*2187 = 4374#

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