In an arithmetic progression the first term is 5 and its common difference is 3. If the general term is an , find a18 - a13.
Question
In an arithmetic progression the first term is 5 and its common difference is 3. If the general term is a_n, find a_{18} - a_{13}.
Solution
In an arithmetic progression, the nth term (an) can be found using the formula:
an = a + (n - 1)d
where: a is the first term, d is the common difference, and n is the term number.
Given that the first term (a) is 5 and the common difference (d) is 3, we can find the 18th term (a18) and the 13th term (a13) as follows:
a18 = a + (18 - 1)d = 5 + (18 - 1)3 = 5 + 51 = 56 a13 = a + (13 - 1)d = 5 + (13 - 1)3 = 5 + 36 = 41
The difference between the 18th term and the 13th term is:
a18 - a13 = 56 - 41 = 15
So, a18 - a13 = 15.
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