The first and the last terms of an A.P. are and respectively. If the sum of all its terms is , then the difference would be?

# The first and the last terms of an A.P. are and respectively. If the sum of all its terms is , then the difference would be?

1. A
2. B
3. C
4. D

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### Solution:

Concept- Using the fact that in an A.P, , and . Solve the two equations to find (the number of terms) and (the common difference).
An arithmetic progression is a number sequence in which adjacent numbers differ by a fixed factor. It is written in the format , and the common difference is .
Given: The first term of an A.P are and the last terms of A.P The Sum of all terms is 420.
Find: We have to find the common difference of the A.P.
Let us assume that be the first term and will be the common difference.
As from the formula, we know that sum of first terms Also,  term According to the question,
and Now,
Also,
We know Thus, common difference of the given A.P. is Hence, the correct option is 3.

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