# How do you find the first four terms of the geometric sequence for which a1=4 and r=3?

Dec 31, 2015

If the first term is 4 and the common ratio (r) is 3, t

#### Explanation:

If the first term is 4 and the common ratio (r) is 3, then the second term must be 3 times the first time, since a geometric series is a repeated multiplication. Alternatively, you can use the formula for the nth of a geometric series, which will benefit when you're dealing with very large numbers such as finding ${t}_{26}$ (the 26th term).

The following solution solves this problem using the formula:

${t}_{n}$ = a • ${r}^{n - 1}$

${t}_{4}$ = 4 • ${3}^{4 - 1}$

${t}_{4}$ = 4 • 27

${t}_{4}$ = 108

The 4th term is 108, and by logical deduction the 3rd term is 36, the second term 12 and the first term 4.

${t}_{1}$ = 4
${t}_{2}$ = 12
${t}_{3}$ = 36
${t}_{4}$ = 108
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