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FAQ (Frequently Asked Questions)

1. What is the formula for the sum of the square of first N natural numbers?

The sum of the square of the first N natural number can be calculated using the following formula-

( n(n+1)(2n+1) /6)

2. What is an AGP series?

The Arithmetic-Geometric Progression (AGP) is a sequence of which each term can be expressed as the product of an arithmetic progression and a geometric progression. The general form of an AGP is-Â Â Â Â Â Â Â

a, (a+d)r,Â (a+2d)r^{2},Â (a+3d)r^{3}, (a+4d)r^{4}, â€¦â€¦â€¦.. (a+(n-1)d)r^{n-1}

Here, â€˜aâ€™ is the first term, â€˜dâ€™ is a common difference and â€˜râ€™ is the common ratio.

3. How can we determine nth term of an arithmetic sequence?

Given an arithmetic sequence with the first term a_{1} and the common difference d, thenÂ the n^{th} (or general) term is determined by an=a_{1}+(n-1)d