Question

An ascending weather balloon starts taking air samples at a height of 30,000 feet and every 1000 feet thereafter. What is its height when it takes the 7th sample?

Answer 1

The height of the balloon can be represented by this sequence:

`30000,31000,32000,\ldots`

Each term of the sequence is related to the previous by the sum of a constant number. This means that this is a arithmetic sequence. The "nth" term of a arithmetic sequence can be found with the expression below:

`a_n=a_1+(n-1)\cdot r`

Where an is the nth term, a1 is the first term, n is the number of terms and r is the constant between the terms. We want to find the 7th term, so n=7.

`\begin{gathered} a_7=30000+(7-1)\cdot1000 \\ a_7=30000+6\cdot1000 \\ a_7=30000+6000 \\ a_7=36000 \end{gathered}`

The 7th term is 36000.