Find 12th term of a geometric sequence whos first two terms are 4 and -8.
In your GS, first two terms are 4 and -8
so ....
a = 4 and
ar = -8 ---> r = -2
term(12) = ar^11 = 4(-2)^11 = .... , you do the arithmetic.
To find the 12th term of a geometric sequence, we need to determine the common ratio (r) first. The common ratio is found by dividing any term in the sequence by the preceding term. Let's calculate it:
r = (-8) / 4
r = -2
Now, we can use the formula to find the nth term of a geometric sequence:
Tn = a * r^(n-1)
where Tn represents the nth term, a is the first term, r is the common ratio, and n is the term number.
Substituting the given values:
T12 = 4 * (-2)^(12-1)
Now, let's simplify the equation:
T12 = 4 * (-2)^11
T12 = 4 * (-2048)
T12 = -8192
Therefore, the 12th term of the geometric sequence is -8192.
To find the 12th term of a geometric sequence, we need to first determine the common ratio (r) of the sequence.
In a geometric sequence, each term is found by multiplying the previous term by the common ratio.
Given that the first term (a₁) is 4 and the second term (a₂) is -8, we can find the common ratio (r) using the formula:
r = a₂ / a₁
Substituting the values, we get:
r = -8 / 4 = -2
Now that we know the common ratio (r = -2), we can find the 12th term (a₁₂) using the formula:
a₁₂ = a₁ * r^(n-1)
where n is the position of the term we want to find, in this case, n = 12.
Substituting the values, we get:
a₁₂ = 4 * (-2)^(12-1)
= 4 * (-2)^11
Now, we can simplify the expression. Since (-2)^11 is a negative exponent, we can rewrite it as:
(-2)^11 = -1 * (2)^11
Now we can calculate the value:
a₁₂ = 4 * (-1) * (2^11)
= -4 * 2048
= -8192
Therefore, the 12th term of the geometric sequence is -8192.