Find the 10th term of the arithmetic progression whose 4th term is 7 and whose 17th term is 72.a.47b.42c.32d.37
Question
Find the 10th term of the arithmetic progression whose 4th term is 7 and whose 17th term is 72.a.47b.42c.32d.37
Solution
The formula for the nth term of an arithmetic progression is a + (n - 1)d, where a is the first term and d is the common difference.
First, we need to find the common difference. We know the 4th term (a + 3d) is 7 and the 17th term (a + 16d) is 72.
Subtract the 4th term from the 17th term to get:
72 - 7 = (a + 16d) - (a + 3d) 65 = 13d d = 65 / 13 d = 5
Now that we know the common difference, we can find the first term (a) by rearranging the formula for the 4th term:
7 = a + 3d 7 = a + 3*5 7 = a + 15 a = 7 - 15 a = -8
Now we can find the 10th term using the formula a + (n - 1)d:
10th term = a + (10 - 1)d 10th term = -8 + 9*5 10th term = -8 + 45 10th term = 37
So, the 10th term of the arithmetic progression is 37 (option d).
Similar Questions
Thirteen times the thirteenth term of an arithmetic progressions equal to seven times the seventh term of the arithmetic progression. What is the twentieth term?a.- 1b.- 3c.0d.4
An arithmetic series seventh term is 27 and thirteenth term is 45.Find the twentieth term of the series.3 marks
What is the 15th term of an arithmetic progression whose first term is equal to its common difference and whose 3rd term is 9.a.45b.15c.60d.30
The sixth term and the eleventh term of a arithmetic progression are 30 and 55 respectively. Find the twenty-first term of the series.a.92 ½b.110c.105d.88 1/3
The sum of five terms of an arithmetic progression is 70. The product of the extreme terms is 132. Find the five terms.a.8, 12, 16, 20, 24b.10, 12, 14, 16, 18c.4, 8, 12, 16, 20d.6, 10, 14, 18, 22
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.