find the 20th term of an arithmetic progression whose 6th term is 3 and 14th term is 19
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The 20th term is 31.
find the
To find the 20th term of an arithmetic progression, we need to identify the common difference (d) of the sequence and use the formula for the nth term of an arithmetic progression, which is:
an = a1 + (n - 1) * d
where:
an is the nth term
a1 is the first term
n is the position of the term in the sequence
d is the common difference
Step 1: Find the common difference (d)
We are given the 6th term and the 14th term. We can use these terms to find the common difference. Let's denote the 6th term as a6 and the 14th term as a14.
a6 = 3 (given)
a14 = 19 (given)
We can calculate the common difference (d) using the formula:
d = (a14 - a6) / (14 - 6)
d = (19 - 3) / (14 - 6)
d = 16 / 8
d = 2
Therefore, the common difference (d) is 2.
Step 2: Find the 20th term (a20)
Now that we know the common difference (d), we can use the formula for the nth term to find the 20th term (a20):
a20 = a1 + (20 - 1) * d
Since we don't have the value of the first term (a1), we need to find it. We can calculate a1 using the formula:
a1 = a6 - (6 - 1) * d
a1 = 3 - (6 - 1) * 2
a1 = 3 - 5 * 2
a1 = 3 - 10
a1 = -7
Now, substitute the values of a1 and d into the formula for a20:
a20 = - 7 + (20 - 1) * 2
a20 = -7 + 19 * 2
a20 = -7 + 38
a20 = 31
Therefore, the 20th term of the arithmetic progression is 31.