Find the 10th term of the geometric sequence 3, 12, 48, …

Ashleigh Clarke

Ashleigh Clarke

Answered question

2022-10-14

Find the 10th term of the geometric sequence 3, 12, 48, …

Answer & Explanation

Miah Scott

Miah Scott

Beginner2022-10-15Added 19 answers

A geometric sequence is a sequence of the form
a , a r , a r 2 , a r 3 , ...
where a is an initial value and r is a common factor between terms.
Looking at this, we can tell that the nth term will be of the form a r n - 1 and so the 10th term will be a r 9 .
In the given sequence, we start at 3 and thus a=3.
To find r we need only divide a term by the term prior to it. So, for example, dividing the second term by the first gives us
r = a r a = 12 3 = 4
Thus the 10th term is 3 4 9 = 786432

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