Write a rule for the nth term of the geometric sequence, then find a6 given 2, 4/3, 8/9, 16/27,...

Marilyn Cameron

Marilyn Cameron

Answered question

2022-10-16

Write a rule for the nth term of the geometric sequence, then find a6 given 2, 4/3, 8/9, 16/27,...

Answer & Explanation

blackcat1314xb

blackcat1314xb

Beginner2022-10-17Added 19 answers

The first term is given as 2, so a=2
The common ration, r is found by dividing 2 consecutive terms..
r = T n T n - 1 In other words, a term divided by the one before it.
r = 4 3 ÷ 2 1 = 4 3 × 1 2 = 2 3
Check: r = 8 9 ÷ 4 3 = 8 9 × 3 4 = 2 3
Now, knowing the values for a and r, we can substitute into the general form for a term of a GP
T n = a r n - 1 2 × ( 2 3 ) n - 1
Simplifying gives: T n = 2 n 3 n - 1
In the same way we can find a 6 = a r 5
But we have already found the general form, so let's use that for n=6
T 6 = 2 6 3 5
T 6 = 64 243

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