Given a(n) = a + d(n - 1), find the value of a and d for the arithmetic sequence 3, 5, 7, 9, …?

Solution:

Given: Series is 3, 5, 7, 9, …..

On observing we got that the series is an Arithmetic Progression

An Arithmetic Progression is a sequence of numbers in which each number differs from the preceding one by a constant quantity.

Eg: 1, 2, 3, 4, 5

Here the difference between every number is 1

Therefore, this is in AP.

Eg: 2, 4, 6, 8

Here the difference between every number is 2

Therefore, this is in AP.

Now,

In the given series we have 3, 5, 7, 9…

Here the difference between every number is 2

Therefore, it is in AP

Also given a formula a(n) = a + d(n - 1)

Here a is denoted for the first term of an AP and d is denoted for the common difference

For the given sequence we get,

a = 3 and d = 2

Summary:

For the given arithmetic series 3, 5, 7, 9… the values of a and d are 3 and 2.

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