1.What is the 10th term of 1/2, 1, 3/2, 5/2
2. What is the 15th term of 0.3, 0.9, 0.15
3. What is the 80th term of 8, 13, 21, 29
you must know that
term(n) = a + (n-1)d, where n is the term number, a is the first term and d is the common difference
so, for the first one:
n = 10, a = 1/2, d = 1/2
term(1) = 1/2 + 9(1/2) = 5
follow the same method for #2
#3 appears to have a typo, it is neither an arithmetic, nor a geometric sequence.
Did you mean: 5, 13, 21, 29 ??
then a = 5, d = 8
To find the nth term of a sequence, we need to identify the pattern or rule followed by the sequence. Let's look at each of the questions and find the pattern to determine the nth terms.
1. The given sequence is: 1/2, 1, 3/2, 5/2.
By observing the sequence, we can see that each term is increasing by 1/2. Therefore, the pattern is an arithmetic sequence with a common difference of 1/2.
To find the 10th term of this sequence, we use the formula for the nth term of an arithmetic sequence:
nth term = first term + (n - 1) * common difference.
In this case:
first term = 1/2,
common difference = 1/2,
n = 10.
Plugging in the values, we get:
nth term = 1/2 + (10 - 1) * 1/2 = 1/2 + 9/2 = 10/2 = 5.
Therefore, the 10th term of the sequence is 5.
2. The given sequence is: 0.3, 0.9, 0.15.
The pattern in this sequence is a bit more complicated. If we observe closely, we can see that each term is obtained by multiplying the previous term by 3 and then dividing it by 10.
Let's find the formula for the nth term:
nth term = first term * (common ratio)^(n - 1).
In this case:
first term = 0.3,
common ratio = 3/10,
n = 15.
Calculating the 15th term, we have:
nth term = 0.3 * (3/10)^(15 - 1) = 0.3 * (3/10)^14.
Evaluating this expression, we find the 15th term of the sequence.
3. The given sequence is: 8, 13, 21, 29.
The pattern here is more apparent. If we look at the sequence, we can see that each term is obtained by adding 5 to the previous term.
This sequence follows an arithmetic pattern with a common difference of 5.
Using the same formula for an arithmetic sequence, we can find the 80th term:
nth term = first term + (n - 1) * common difference.
In this case:
first term = 8,
common difference = 5,
n = 80.
Plugging in the values, we have:
nth term = 8 + (80 - 1) * 5 = 8 + 79 * 5.
Evaluating this expression will give us the 80th term of the sequence.
Remember, it is essential to identify the pattern or rule of the given sequence to find the nth term accurately.