the sixth term of an AP is 35 and 13th term is 77.find the 20th term.
The 6th term of an A.P is 35 and the 13th term is 77. Find the 20th term.
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To find the 20th term of the Arithmetic Progression (AP), you need to determine the common difference (d) first. Here's how you can do it:
1. Find the difference between the 13th term and the 6th term:
d = 77 - 35
d = 42
This means that the common difference between consecutive terms in the AP is 42.
2. Formula to find the nth term (where n represents the term number) in an AP:
an = a1 + (n - 1) * d
In this formula, "an" represents the nth term, "a1" represents the first term, and "d" represents the common difference.
3. Plug in the values to find the 20th term:
a20 = a1 + (20 - 1) * d
Since the 6th term is given as 35 (a6 = 35), we can use it as the first term (a1).
a20 = 35 + (20 - 1) * 42
a20 = 35 + 19 * 42
a20 = 35 + 798
a20 = 833
Therefore, the 20th term of the Arithmetic Progression is 833.
note that a13-a6 = 7d = 77-35 = 42
a20 = a13 + 7d = 77 + 42