Which term of the geometric sequence 2,-6,18 ....... 162
general term of GS is ar^(n-1)
for yours, a = 2, r = -3
general term = 2(-3)^(n-1) = 162
(-3)^(n-1) = 81 , but I know (-3)^4 = 81
n-1 = 4
n = 5 , so 162 is the 5th term
Reason to write n-1 is equal to 4
5=n
Well, well, well, looks like we've got ourselves a geometric sequence here! Let's do some fun math to find out the term you're looking for, shall we?
So, the first term of the sequence is 2, and if we take a closer look, we can see that each term is multiplied by -3 to get to the next term. (-3 times 2 equals -6, and -3 times -6 equals 18, and so on.)
To find the term you're after, we need to figure out how many times we multiply the first term (2) by -3. We can do that by taking the given term (162) and dividing it by the first term (2):
162 ÷ 2 = 81
So it seems like the term you're looking for is 81. Voilà!
Now, wasn't that an amusing way to find the answer? Keep those math questions coming, and I'll keep the humor flowin'!
To find the term of a geometric sequence, we need to determine the common ratio (r) first. The common ratio is found by dividing any term by its previous term.
For example, let's take the second and first terms:
-6 / 2 = -3.
So, the common ratio (r) in this sequence is -3.
Now, we can use the formula for the nth term (Tn) of a geometric sequence to find the desired term:
Tn = a * r^(n-1),
Where:
- Tn is the nth term of the sequence,
- a is the first term, and
- r is the common ratio.
In our case, the first term (a) is 2 and the common ratio (r) is -3.
Now, we need to find the value of n for the sequence to be 162. We can start with the first term and multiply it by the common ratio to determine the subsequent terms until we reach the desired term.
2 * (-3) = -6 (2nd term)
-6 * (-3) = 18 (3rd term)
18 * (-3) = -54 (4th term)
-54 * (-3) = 162 (5th term).
So, the desired term of the geometric sequence is 162, and it is the 5th term (n = 5).
Therefore, the answer is the 5th term.