Find the 22nd term of the arithmetic progression whose first term is 20 and common difference is 1/3.a.27 2/3b.27c.27 1/3d.28
Question
Find the 22nd term of the arithmetic progression whose first term is 20 and common difference is 1/3.
Options:
- a. 27 2/3
- b. 27
- c. 27 1/3
- d. 28
Solution
The formula for the nth term of an arithmetic progression is given by:
a_n = a + (n - 1) * d
where: a_n is the nth term a is the first term d is the common difference n is the position of the term in the sequence
Given that the first term (a) is 20 and the common difference (d) is 1/3, we can find the 22nd term (a_22) as follows:
a_22 = a + (22 - 1) * d = 20 + 21 * (1/3) = 20 + 7 = 27
So, the 22nd term of the arithmetic progression is 27. Therefore, the correct answer is (b) 27.
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