An arithmetic series seventh term is 27 and thirteenth term is 45.Find the twentieth term of the series.3 marks

Step 1: Understand the problem An arithmetic series is a sequence of numbers in which the difference of any two successive members is a constant. This constant difference is also known as the common difference. In this problem, we are given the 7th term (27) and the 13th term (45) of an arithmetic series. We are asked to find the 20th term of the series.

Step 2: Find the common difference The common difference (d) can be found by subtracting the 7th term from the 13th term and then dividing by the difference in their positions (13 - 7 = 6). So, d = (45 - 27) / 6 = 3.

Step 3: Find the first term The first term (a) can be found by subtracting 6 times the common difference from the 7th term. So, a = 27 - 6*3 = 9.

Step 4: Find the 20th term The nth term of an arithmetic series can be found using the formula a + (n - 1)*d. Substituting a = 9, d = 3, and n = 20, we get the 20th term = 9 + (20 - 1)*3 = 66.