Question

The 4th term of an exponential sequence is 108 and the common ratio is 3. Calculate the value of the eighth term of the sequence.

Answer 1

Term n = a r^(n-1)
they tell us r = 3
Term n = a * 3^(n-1)
Term 4 = a * 3^3 = 27 a = 108
so
a = 4
so in general
Tn = 4 * 3 ^(n-1)
T8 = 4 * 3^7 = 4 * 2187 = 8748
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Answer 2

We can use the formula for the nth term of an exponential sequence:

a_n = a_1 * r^(n-1)

where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the term number.

We are given that the 4th term is 108 and the common ratio is 3. So we can use these values to find the first term:

a_4 = a_1 * 3^(4-1)
108 = a_1 * 3^3
a_1 = 4

Now we can use this value of a_1 and the common ratio to find the eighth term:

a_8 = a_1 * 3^(8-1)
a_8 = 4 * 3^7
a_8 = 4 * 2187
a_8 = 8748

Therefore, the value of the eighth term of the sequence is 8748.