Find the 10th term of the arithmetic progression whose 4th term is 7 and whose 17th term is 72.a.42b.47c.32d.37
Question
Find the 10th term of the arithmetic progression whose 4th term is 7 and whose 17th term is 72.a.42b.47c.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 equation from the 17th term equation to get:
72 - 7 = (a + 16d) - (a + 3d) 65 = 13d d = 65 / 13 d = 5
Now, substitute d = 5 into the 4th term equation to find a:
7 = a + 3*5 7 = a + 15 a = 7 - 15 a = -8
Now that we have a = -8 and d = 5, we can find the 10th term:
a + (n - 1)d = -8 + (10 - 1)5 = -8 + 95 = -8 + 45 = 37
So, the 10th term of the arithmetic progression is 37. The answer is (d) 37.
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