Geometric Sequence Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
In a geometric sequence, a2=6a_2 = 6 and a5=48a_5 = 48. Find a1a_1 and rr.

Solution

  1. 1
    a1r=6a_1 r = 6 and a1r4=48a_1 r^4 = 48.
  2. 2
    Divide: r3=8⇒r=2r^3 = 8 \Rightarrow r = 2.
  3. 3
    a1=6/2=3a_1 = 6/2 = 3.

Answer

a1=3a_1 = 3, r=2r = 2
Dividing the two equations eliminates a1a_1, leaving a power of rr to solve. Then back-substitute.

About Geometric Sequence

A sequence where each term is obtained from the previous by multiplying by a fixed non-zero constant called the common ratio rr.

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More Geometric Sequence Examples

Example 1 easy

A geometric sequence has [formula] and [formula]. Find [formula] and [formula].

Example 2 medium

Bacteria double every 3 hours. Starting with 500, how many after 15 hours?

Example 3 easy

Find [formula] and [formula] for the sequence [formula]

Example 5 medium

Find the 6th term of the geometric sequence: 2, 6, 18, ...

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