In a geometric sequence, the first term is 2 and the fourth term is 250. Find thei. common ratio of this sequence. (3 Marks)ii. 7th term of this sequence.
Question
In a geometric sequence, the first term is 2 and the fourth term is 250. Find the
i. common ratio of this sequence.
ii. 7th term of this sequence.
Solution
i. In a geometric sequence, the ratio between any term and the previous term is constant. This is known as the common ratio.
The formula for the nth term of a geometric sequence is a * r^(n-1), where a is the first term, r is the common ratio, and n is the term number.
Given that the first term (a) is 2 and the fourth term is 250, we can set up the equation:
2 * r^(4-1) = 250 2 * r^3 = 250 r^3 = 250 / 2 r^3 = 125 r = cuberoot(125) r = 5
So, the common ratio of this sequence is 5.
ii. To find the 7th term of the sequence, we can use the formula for the nth term of a geometric sequence:
a * r^(n-1) = 2 * 5^(7-1) = 2 * 5^6 = 2 * 15625 = 31250
So, the 7th term of this sequence is 31250.
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