Find the sum of the eight term of 12,6,3

Answer 1

To find the sum of the eighth term, we need to determine the pattern in the given sequence.
Starting with 12, the common ratio between each term is 1/2.
So, the next term after 12 is (12)(1/2) = 6.
The next term after 6 is (6)(1/2) = 3.
The next term after 3 is (3)(1/2) = 3/2.
We can observe that the sequence alternates between 3 and 3/2.

To find the eighth term, we start at 12 and repeatedly divide by 2 a total of 3 times, since we are looking for the eighth term. This gives us:

(12)(1/2)(1/2)(1/2) = 12/8 = 3/2

So, the eighth term is 3/2.

To find the sum of the eighth term, we add up all the terms in the given sequence. The sum of n terms in a geometric sequence can be found using the formula:

Sn = a(1 - r^n) / (1 - r)

Where Sn is the sum of the n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = 12, r = 1/2, and n = 8.

Plugging in these values into the formula, we get:

S8 = 12(1 - (1/2)^8) / (1 - 1/2)

Simplifying, we have:

S8 = (12 - 3/256) / (1/2)

Multiplying by the reciprocal, we get:

S8 = (12 - 3/256)(2/1)

S8 = (24 - 3/128)

Now we can convert 24 to a fraction with the same denominator:

S8 = (3072/128 - 3/128)

S8 = (3069/128)

Thus, the sum of the eighth term is 3069/128.