A snail crawled 36 inches in one hour, 24 inches in the next hour, 16 the third hour, and so on. If the snail continues with this pattern forever, then
a) find the total distance the snail traveled.
b) Write the series in summation notation.
Please show the work, thanks in advance
a) find the total distance the snail traveled.
b) Write the series in summation notation.
Please show the work, thanks in advance
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This is geometric : a1= 36, a2=24, a3= 16
r = 24/36= 2/3
A) The infinite sum :
S= a1/(1-r)= 36/(1-2/3)
S= 36* 3= 108 Inches
B) using a1(r)^(n-1) as a pattern:
∞
Σ36(2/3)^(i-1)
i=1
Hoping this helps!
r = 24/36= 2/3
A) The infinite sum :
S= a1/(1-r)= 36/(1-2/3)
S= 36* 3= 108 Inches
B) using a1(r)^(n-1) as a pattern:
∞
Σ36(2/3)^(i-1)
i=1
Hoping this helps!
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Ok. First list your terms and look for a common pattern.
36 24 16
So far I'm noticing that the next term is 2/3 of the last term. So let's continue that pattern and try to find a sum for it.
36 + 24 + 16 + 32/3 + 64/9 + 128/27 + 256/81....
If the snail continues forever, there will be no end to the distance it travels, so the answer is infinity. Granted after a while the snail will be moving incredibly slow. If you were to write this in summation notation, you would write it as
Sigma n = 0 to infinity K = 36+ 2/3 * K(n-1)
36 24 16
So far I'm noticing that the next term is 2/3 of the last term. So let's continue that pattern and try to find a sum for it.
36 + 24 + 16 + 32/3 + 64/9 + 128/27 + 256/81....
If the snail continues forever, there will be no end to the distance it travels, so the answer is infinity. Granted after a while the snail will be moving incredibly slow. If you were to write this in summation notation, you would write it as
Sigma n = 0 to infinity K = 36+ 2/3 * K(n-1)