Nigel is participating in a read-a-thon. The number of pages he reads each night follows a geometric sequence. On the second day of the read-a-thon, Nigel read 8 pages. On the fifth day of the read-a-thon, he read 64 pages. Write an explicit formula to represent this scenario.
Explicit Formula: an=a1 * r^(n-1)
Answer: an=4(2)^n-1
I just don't know how to get to the answer with the information given.
Any ideas?
Can someone delete the question, please? Thank You.
a r^0 ar^1 ar^2 ar^3 ar^4 ar^5
a ar^1=8 ...... ar^4 = 64
so
ar^4/ar^1 = 64/8 = 8
r^3 = 8
r = 2 which we could have guessed when we saw 8 and 64
if ar = 8 and r = 2 then a =4
so
4 *2^(n-1)
To find the explicit formula for the number of pages Nigel reads each night, we need to determine the common ratio of the geometric sequence.
First, let's find the common ratio (r) by dividing the number of pages on the fifth day by the number of pages on the second day:
r = (number of pages on the fifth day) / (number of pages on the second day)
= 64 / 8
= 8
Now that we have the common ratio, we can write the explicit formula for the geometric sequence:
aₙ = a₁ * r^(n-1)
where aₙ represents the number of pages on the nth day, a₁ represents the number of pages on the first day, r represents the common ratio, and n represents the nth term in the sequence.
In this scenario, the number of pages Nigel reads on the second day is 8, so a₁ = 8.
Therefore, the explicit formula to represent this scenario is:
aₙ = 8 * 8^(n-1)