Find the values of s1 and r for a geometric sequence with s4 = 18 and s6= 8
1 answer:
Answer:
see below
Step-by-step explanation:
The ratio of terms that are two terms apart (s4 and s6) is the square of the common ratio:
s6/s4 = r^2
r = √(8/18)
r = 2/3 . . . . . matches choices A and C
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Using the formula for the general term, we now know enough to find the first term:
sn = s1·r^(n-1)
s4 = s1·(2/3)^(4-1)
Using s4 = 18 and multiplying by (2/3)^-3, we get ...
18·(2/3)^-3 = s1 = 18·27/8
s1 = 243/4 . . . . . matches choice A
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Answer:
Average speed of the particle is 13 miles per hour.
Step-by-step explanation:
From the given question expression for distance traveled by the particle is
Then fro the time interval (1, 4) we have to calculate the average speed.
At t=1, s=2(1)²+3(1) =2+3 =5 miles
And at t = 4 s=2(4)²+3(4) = 2(16)+12 = 32+12 =44 miles
So displacement of the particle in the time span from 1 to hours.
s = (44-5) = 39 miles
And the times taken = (4-1) =3 hours
From the formula speed = displacement/(time taken for displacement)
V = 39/3 = 13 miles/hour