The fifth term of an exponential is 4375 and the second term is 35, find
i) the 3 term
ii) the sum of the first five terms
wrong yet again! t5/t2 = r^3, so
r^3 = 125
r = 5
t3 = t2 * r = 35 * 5 = 175
t1 = t2/r = 35/5 = 7
S5 = t1*(r^5-1)/(r-1) = 7(5^5-1)/(5-1) = 5467
Apologies for the previous incorrect response.
You are correct, to find the common ratio (r) of the exponential sequence, we need to take the cube root of the ratio between the fifth term and the second term, which gives us r = 5.
i) To find the third term, we can multiply the second term (t2) by the common ratio (r):
t3 = t2 * r = 35 * 5 = 175
ii) To find the sum of the first five terms, we can use the formula for the sum of a geometric series:
Sum = t1 * (r^n - 1) / (r - 1)
where:
t1 = first term
r = common ratio
n = number of terms
For the first five terms:
t1 = 7
r = 5
n = 5
Sum = 7 * (5^5 - 1) / (5 - 1)
Sum = 7 * (3125 - 1) / 4
Sum = 7 * 3124 / 4
Sum = 5467.
To find the common ratio (r) of the exponential sequence, we can divide the fifth term by the second term:
r = (4375/35) = 125
i) To find the third term, we can multiply the second term by the common ratio:
3rd term = 35 * 125 = 4375
ii) To find the sum of the first five terms, we can use the formula for the sum of a geometric series:
Sum = (a * (r^n - 1)) / (r - 1)
where:
a = first term
r = common ratio
n = number of terms
For the first five terms:
a = 35
r = 125
n = 5
Sum = (35 * (125^5 - 1)) / (125 - 1)
Sum = (35 * (9,765,625 - 1)) / 124
Sum = (35 * 9,765,624) / 124
Sum = 2,734,375