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Sequences and Series

What's the sum of the first 100 positive integers? How about the first 1000?

Arithmetic Progressions

         

Which of the following sequences is an Arithmetic Progression?

Suppose that when you are a teenager, your height increases at a steady rate of 3 inches every year. If your present height is 48 inches, then how many years will you take to grow to 66 inches tall?

The figure shows the concentric circles with radii \( 1, 3,5,7, \ldots\) and so on. Find the area of 18th circle.

In the arithmetic progression \[-110, -107, -104, \cdots,\] the \(n^\text{th}\) term \(a_n\) is the first positive number. What is \(n\)?

A sequence \(\{a_n\}\) is defined as \[a_1=12, a_{n+1}=a_n+3,\] where \(n \in \mathbb{N}.\) What is the general term of \(\{a_n\} ?\)

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