Find the tenth term of the sequence: -6,1,8...
Is it 57?
For the sequence:2,4,8,16 the value of s4 is____.
Is it 8?
Find the 7th term of the sequence: 1,2,4,...
Is it 64?
Which term of this sequence is 275?
5,10,15,...
Is it 1357?
Find the 7thterm of an. Arithmetic sequence whose first term is -8and whose common difference is 3.
Is it 10?
For the sequence: -6, 1, 8...
To find the n-th term of an arithmetic sequence, we use the formula: an = a1 + (n - 1)d
Here, a1 (the first term) is -6 and d (the common difference) is 1.
So, for the 10th term (n = 10), we have: a10 = -6 + (10 - 1)(1) = -6 + 9 = 3
Therefore, the 10th term of the sequence -6, 1, 8... is 3.
No, it is not 57.
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For the sequence: 2, 4, 8, 16
Here, a1 = 2 and d = 4 - 2 = 2 (the common difference).
Using the formula an = a1 + (n - 1)d, we can find the value of s4 (the 4th term).
Therefore, s4 = 2 + (4 - 1)(2) = 2 + 6 = 8
Yes, s4 (the 4th term) of the sequence 2, 4, 8, 16 is 8.
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For the sequence: 1, 2, 4, ...
Here, a1 = 1 and d = 2 - 1 = 1 (the common difference).
Using the formula an = a1 + (n - 1)d:
For the 7th term (n = 7), we have: a7 = 1 + (7 - 1)(1) = 1 + 6 = 7
Therefore, the 7th term of the sequence 1, 2, 4... is 7.
No, it is not 64.
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For the sequence: 5, 10, 15...
Here, a1 = 5 and d = 10 - 5 = 5 (the common difference).
Using the formula an = a1 + (n - 1)d:
To find the term that equals 275, we need to solve the equation:
275 = 5 + (n - 1)(5)
275 = 5 + 5n - 5
275 = 5n
n = 55
Therefore, the term that equals 275 in the sequence 5, 10, 15... is 55.
No, it is not 1357.
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For the arithmetic sequence with a first term of -8 and a common difference of 3:
Using the formula an = a1 + (n - 1)d,
For the 7th term (n = 7), we have: a7 = -8 + (7 - 1)(3) = -8 + 6(3) = -8 + 18 = 10
Therefore, the 7th term of the arithmetic sequence with the first term -8 and common difference 3 is 10.
Yes, it is 10.
To find the tenth term of a sequence, we need to identify the pattern in the sequence and use that pattern to determine the value of the tenth term.
For the sequence -6, 1, 8..., we can see that each term is obtained by adding 7 to the previous term. Thus, the pattern is an arithmetic sequence with a common difference of 7.
To find the tenth term, we start with the first term, which is -6, and then add 7 successively nine times to get the subsequent terms.
-6 + 7 = 1
1 + 7 = 8
8 + 7 = 15
15 + 7 = 22
22 + 7 = 29
29 + 7 = 36
36 + 7 = 43
43 + 7 = 50
50 + 7 = 57
So, the tenth term of the given sequence is indeed 57.
For the sequence 2, 4, 8, 16, to find the value of s4 (the fourth term), we follow the same process. Each term in this sequence is obtained by doubling the previous term.
2 × 2 = 4
4 × 2 = 8
8 × 2 = 16
So, the fourth term is indeed 16.
For the sequence 1, 2, 4..., the pattern is a geometric sequence where each term is obtained by multiplying the previous term by 2.
2^0 = 1
2^1 = 2
2^2 = 4
2^3 = 8
So, the seventh term is indeed 8.
For the sequence 5, 10, 15..., to find which term is 275, we again look for the pattern. In this case, the pattern is an arithmetic sequence with a common difference of 5.
To find the term that equals 275, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.
In this case:
a1 = 5
d = 5
Let's plug in the values and solve for n:
275 = 5 + (n - 1)5
275 = 5 + 5n - 5
275 = 5n
Dividing both sides by 5:
55 = n
So, the term that equals 275 is indeed 55, not 1357.
For the arithmetic sequence with a first term of -8 and a common difference of 3, we can use the same formula to find the nth term.
a1 = -8
d = 3
Using the formula:
an = a1 + (n - 1)d
Let's plug in the values and solve for the seventh term (n = 7):
a7 = -8 + (7 - 1)3
a7 = -8 + 6 × 3
a7 = -8 + 18
a7 = 10
So, the seventh term of the given arithmetic sequence is indeed 10.