write an explicit formula to find the 10th term of each geometric sequence. -3,6,-12,24
is that correct
AAAaannndd the bot gets it wrong yet again!
a_10 = ar^9 = (-3)(-2)^9 = 1536
I apologize for the mistake in my previous response. The correct formula for the nth term in a geometric sequence with first term 'a' and common ratio 'r' is:
an = a * r^(n-1)
Using this formula, we can find the 10th term in the sequence -3, 6, -12, 24 as:
a10 = (-3) * (-2)^(10-1)
a10 = (-3) * (-2)^9
a10 = (-3) * (-512)
a10 = 1536
Hence, the 10th term in the given sequence is 1536. I apologize for any confusion caused.
To find the explicit formula for the 10th term of a geometric sequence, we need the first term and the common ratio.
In this sequence, the first term is -3, and the common ratio can be found by dividing any term by its previous term.
Dividing 6 by -3, we get -2. Similarly, dividing -12 by 6 gives us -2, and dividing 24 by -12 also gives us -2.
Therefore, the common ratio (r) is -2.
The explicit formula for the nth term of a geometric sequence is given by the formula:
an = a1 * r^(n-1)
where an represents the nth term, a1 is the first term, r is the common ratio, and n is the term number.
Plugging in the given values, we have:
a10 = -3 * (-2)^(10-1)
Simplifying this expression, we get:
a10 = -3 * (-2)^9
Calculating this further, we find:
a10 = -3 * (-512)
Finally, evaluating the expression, we get:
a10 = 1536
Therefore, the 10th term of the given geometric sequence is 1536.
To find the explicit formula for a geometric sequence, we need to determine the common ratio (r).
In the given sequence, we can observe that each term is obtained by multiplying the previous term by -2. Hence, the common ratio (r) is -2.
Now, we can use the general formula for the nth term of a geometric sequence:
an = a1 * r^(n-1)
Here, "an" represents the nth term of the sequence, "a1" is the first term, "r" is the common ratio, and "n" is the position of the term we want to find.
Plugging in the values from the given sequence:
a1 = -3 (first term)
r = -2 (common ratio)
To find the 10th term (an), we substitute n = 10 into the formula:
a10 = -3 * (-2)^(10-1)
Now, we simplify this expression:
a10 = -3 * (-2)^9
a10 = -3 * (-512)
a10 = 1536
Therefore, the 10th term of the given geometric sequence is 1536.
The common ratio between consecutive terms in this sequence is -2, so the nth term can be expressed as:
an = (-3) * (-2)^(n-1)
To find the 10th term, we plug in n = 10:
a10 = (-3) * (-2)^(10-1)
a10 = (-3) * (-2)^9
a10 = (-3) * (-512)
a10 = 1536
Therefore, the 10th term of the sequence -3, 6, -12, 24 is 1536.