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
Question
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. 45
b. 15
c. 60
d. 30
Solution
The first term (a) of the arithmetic progression is equal to the common difference (d). Given that the third term is 9, we can use the formula for the nth term of an arithmetic progression:
nth term = a + (n-1)d
Substituting the given values:
9 = a + (3-1)a 9 = 2a a = 9/2 = 4.5
So, the common difference d is also 4.5.
Now, to find the 15th term, we substitute these values into the formula:
15th term = a + (15-1)d 15th term = 4.5 + (14)*4.5 15th term = 4.5 + 63 15th term = 67.5
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