Find the 21st term of the Arithmetic Progression (A.P.): -4, -1.5, 1, 3.5,...
Answer Details
We are given the first four terms of an Arithmetic Progression (A.P.) and we are required to find the 21st term. We can notice that the common difference between any two successive terms is \(d = -1.5 - (-4) = 2.5\).
Using the formula for the nth term of an A.P., which is given by:
\(a_{n} = a_{1} + (n - 1) d\)
where \(a_{n}\) is the nth term, \(a_{1}\) is the first term, \(n\) is the number of terms and \(d\) is the common difference.
We can now find the 21st term as follows:
\(a_{21} = a_{1} + (21 - 1) d\)
Substituting the given values, we get:
\(a_{21} = -4 + (21 - 1) \times 2.5 = 46\)
Hence, the 21st term of the given A.P. is 46. Therefore, the correct option is (B) 46.