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Question
If the first term of an A.P. is a and nth term is b, then its common difference is
Options
- \[\frac{b - a}{n + 1}\]
- \[\frac{b - a}{n - 1}\]
- \[\frac{b - a}{n}\]
- \[\frac{b + a}{n - 1}\]
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Solution
Here, we are given the first term of the A.P. as a and the nth term (an) as b. So, let us take the common difference of the A.P. as d.
Now, as we know,
an = a + ( n-1) d
On substituting the values given in the question, we get.
b = a + ( n - 1) d
( n - 1) d = b - a
d = \[\frac{b - a}{n - 1}\]
Therefore, d = \[\frac{b - a}{n - 1}\]
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