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Nikitich [7]
3 years ago
7

What is the 50th term of the sequence that begins with -6, 0, 6, 12...

Mathematics
1 answer:
vazorg [7]3 years ago
5 0

Answer:

The 50th term is 288.

Step-by-step explanation:

A sequence that each term is related with the prior by a sum of a constant ratio is called a arithmetic progression, the sequence in this problem is one of those. In order to calculate the nth term of a setence like that we need to use the following formula:

an = a1 + (n-1)*r

Where an is the nth term, a1 is the first term, n is the position of the term in the sequence and r is the ratio between the numbers. In this case:

a50 = -6 + (50 - 1)*6

a50 = -6 + 49*6

a50 = -6 + 294

a50 = 288

The 50th term is 288.

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3 years ago
A population of butterflies grows in such a way that each generation is simply 1.5 times the previous generation. There were 350
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Answer:

378.5 or just 378

Step-by-step explanation:

This is a linear model with x representing the number of generations that's gone by, y is the number of butterflies after x number of generations has gone by, and the 350 represents the number of butterflies initially (before any time has gone by.  When x = 0, y = 350 so that's the y-intercept of our equation.)

The form for a linear equation is y = mx + b, where m is the rate of change and b is the y-intercept, the initial amount when x = 0.

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If we want y when x = 19, plug 19 in for x and solve for y:

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