Find the recursive definition of the following sequence (remember to define the first term t, the recursive rule to find tn, and the value n will start at.) 1, 6, 36, 216, 1296…..

The answer is composed of the following two equations

and

both of these two equations combine to help form the full recursive definition

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Further explanation:

The terms are represented by the letter 't' for short. Since we have more than one term, and because we have only so many letters, this means we stick a number onto the 't' to help label multiple terms. We have t1 as the first term, t2 as the second, etc. The numbers are often show as subscripts like so

The first term of the list of numbers is 1, so is what we start with to help set up the recursive definition.

Once we have this starting point, we use it to get to the next term which is 6. This value is 6 times the first value. Therefore, the recursive step is basically saying "multiply the (n-1)st term by 6 to get the nth term. Translation:  "whatever the current term is, multiply by 6 to get the next term".

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation: