The 5th term of an arithmetic progression is 3times of 2nd term and 12th term exceeds 2times of 6th term by 1. Find the 16th term
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To find the 16th term of the arithmetic progression, we need to first determine the common difference.
Let's start by using the given information that the 5th term is three times the 2nd term.
Let the first term of the arithmetic progression be "a" and the common difference be "d."
So, the 5th term can be represented as:
a + 4d
And the 2nd term can be represented as:
a + d
According to the given condition, the 5th term is three times the 2nd term:
a + 4d = 3(a + d)
Now we simplify and solve for "d":
a + 4d = 3a + 3d
4d - 3d = 3a - a
d = 2a
Therefore, we have found that the common difference (d) is equal to 2a.
Next, let's use the second given condition: the 12th term exceeds 2 times the 6th term by 1.
The 12th term can be represented as:
a + 11d
And the 6th term can be represented as:
a + 5d
According to the given condition, the 12th term exceeds 2 times the 6th term by 1:
a + 11d = 2(a + 5d) + 1
Now, let's simplify and solve for "a":
a + 11d = 2a + 10d + 1
10d - 11d = 2a - a + 1
-d = 1
d = -1
Since "d" represents the common difference, we found that the common difference is -1. However, it's not possible to have a negative common difference in an arithmetic progression. Hence, there must have been a mistake in the information provided.
Please check the given information again or provide any additional information if available so that we can proceed to find the correct solution.