In an A.P., if am = and an = , then amn =
Question
In an A.P., if am = and an = , then amn =
Solution
In an arithmetic progression (A.P.), if am = a and an = b, then amn = c.
Step 1: Determine the common difference (d) of the arithmetic progression. To find the common difference, we subtract the previous term from the next term: d = an - am
Step 2: Find the value of amn. Since the common difference is constant, we can use it to find the value of amn. amn = am + (n-1)d
Substituting the given values: amn = a + (n-1)(an - am)
Simplifying further: amn = a + (n-1)(b - a)
Therefore, the value of amn in the arithmetic progression is a + (n-1)(b - a).
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