So we need to find the sum of the first 5 terms.
You have told me that the first term is 10 meters, and that r = 0.5 per term.
With this knowledge, we can use the formula s_n=a₁((1-r^n)/(1-r)).
Plugging in the terms that we know...
s₅=10((1-0.5⁵)/(1-0.5))
s₅=10(0.96875/0.5)
s₅=10(1.9375)
s₅=19.375
With s₅, we can determine that the ball has traveled a total of 19.375 meters after 5 bounces.
For (8, 16): 3(8) - 8 = 24 - 8 = 16 [solution]
For (3, 4): 3(3) - 8 = 9 - 8 = 1 [not a solution]
For (-6, -26): 3(-6) - 8 = -18 - 8 = -26 [solution]
For (-10, -38): 3(-10) - 8 = -30 - 8 = -38 [solution]
I hope I helped! :)
Answer:
a) A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers; b) A series is divergent if it is not convergent. A series is convergent if the sequence of partial sums is a convergent sequence.
Step-by-step explanation:
A sequence is a pattern. It is an ordered list of objects, such as numbers, letters, colors, etc.
A series is a sum of a sequence.
A divergent series is one that is not convergent.
A convergent series is one in which the sequence of partial sums approaches a limit; this means the partial sums form a convergent sequence.
An altitude is a line which passes through a vertex of a triangle, and is at right angles to the opposite side. A triangle has three altitudes.
