the fifth term of an exponentrial sequence is 4375 and the second term is 35, find the third and the sixth term
4375 / 35 = 125 = 5^3
7 * 5^0 , 7 * 5^1 , 7 * 5^2 , 7 * 5^3 , 7 * 5^4 , 7 * 5^5 ...
To find the third term of the exponential sequence, we need to determine the common ratio (r) first.
Given that the second term is 35, we can divide the second term by the first term to find the common ratio:
35 / 1 = 35
Now that we know the common ratio is 35, we can write the general formula for the nth term of an exponential sequence:
an = a1 * r^(n - 1)
Where:
an = nth term
a1 = first term
r = common ratio
n = term number
Let's substitute the known values into the formula to find the third term (a3):
a3 = a1 * r^(3 - 1)
Knowing that the fifth term is 4375, we can find the first term (a1) by calculating it using the formula:
a5 = a1 * r^(5 - 1)
Substituting the known values:
4375 = a1 * r^4
Now, let's solve for a1:
a1 = 4375 / r^4
Now we have both a1 and r, we can substitute them into the formula to find the third term:
a3 = (4375 / r^4) * r^(3 - 1)
Simplifying the equation:
a3 = 4375 / r^2
Now we can plug in the value of r we found earlier (r = 35) to calculate the third term:
a3 = 4375 / 35^2
a3 = 4375 / 1225
a3 = 3.57 (rounded to two decimal places)
Therefore, the third term of the exponential sequence is approximately 3.57.
To find the sixth term, we can again use the general formula for the nth term:
a6 = a1 * r^(6 - 1)
Substituting the known values for a1 and r:
a6 = (4375 / 1225) * 35^5
a6 = 1694000 (rounded to the nearest whole number)
Therefore, the sixth term of the exponential sequence is 1,694,000.