The nth term of an A.P. is given by an = 3 + 4n. The common difference is(a) 7(b) 3(c) 4(d) 1
Question
The nth term of an A.P. is given by . The common difference is
- (a) 7
- (b) 3
- (c) 4
- (d) 1
Solution
The common difference of an arithmetic progression (A.P.) is found by subtracting the (n-1)th term from the nth term.
Given the nth term of an A.P. as an = 3 + 4n, we can express the (n-1)th term as a(n-1) = 3 + 4(n-1).
Subtracting a(n-1) from an gives:
an - a(n-1) = [3 + 4n] - [3 + 4(n-1)] = 4n - 4(n-1) = 4n - 4n + 4 = 4
So, the common difference of the A.P. is 4. Therefore, the correct answer is (c) 4.
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