A sequence is given by the formula of its nth term : an =10−3n. prove that an is an arithmetic progression.
Question
A sequence is given by the formula of its nth term:
Prove that is an arithmetic progression.
Solution
To prove that a sequence is an arithmetic progression, we need to show that the difference between any two consecutive terms is constant.
The nth term of the sequence is given by an = 10 - 3n.
Let's find the (n+1)th term:
an+1 = 10 - 3(n + 1) = 10 - 3n - 3 = an - 3
The difference between the (n+1)th term and the nth term is:
an+1 - an = (an - 3) - an = -3
Since this difference is constant, we can conclude that the sequence is an arithmetic progression.
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