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?
Find the tenth term of the sequence: -6,1,8...
Is it 57? YES
For the sequence:2,4,8,16 the value of s4 is____.
Is it 8? If s4 means the sum of four terms, why not just add them up, they are there in front of you, sum(4) = 30
Find the 7th term of the sequence: 1,2,4,...
Is it 64? YES
Which term of this sequence is 275?
5,10,15,...
Is it 1357? Of course not
term(n) = a + (n-1)d
275 = 5 + (n-1)(5)
270 = 5(n-1)
54 = n-1
n = 55 , it is term(55)
Find the 7thterm of an. Arithmetic sequence whose first term is -8and whose common difference is 3.
Is it 10? YES
5. a tap can fill a tank in 15 minutes .another tap can empty it in 20 minutes. Initially the tank is empty, if both the taps start functioning the same time, when will the tank become fill?
To find the tenth term of the sequence -6, 1, 8..., we can observe that each term is obtained by adding 7 to the previous term. So, the common difference is 7.
To find the tenth term, 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, the first term (a1) is -6, the term number (n) is 10, and the common difference (d) is 7.
Therefore, the tenth term is calculated as follows:
a10 = -6 + (10-1)7
a10 = -6 + 63
a10 = 57
Yes, the tenth term of the sequence -6, 1, 8... is indeed 57.
For the sequence 2, 4, 8, 16, it is a geometric sequence with a common ratio of 2. Each term is obtained by multiplying the previous term by 2.
To find the value of s4, which is the fourth term of the sequence, we can use the formula for the nth term of a geometric sequence: an = a1 * r^(n-1), where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number.
In this case, the first term (a1) is 2, the term number (n) is 4, and the common ratio (r) is 2.
Therefore, the fourth term is calculated as follows:
a4 = 2 * 2^(4-1)
a4 = 2 * 2^3
a4 = 2 * 8
a4 = 16
Yes, the value of s4, the fourth term of the sequence 2, 4, 8, 16, is indeed 16.
To find the seventh term of the sequence 1, 2, 4..., we can observe that each term is obtained by multiplying the previous term by 2. So, it is a geometric sequence with a common ratio of 2.
Using the same formula as before, we can find the seventh term:
a7 = 1 * 2^(7-1)
a7 = 1 * 2^6
a7 = 1 * 64
a7 = 64
No, the seventh term of the sequence 1, 2, 4... is 64, not 57.
To find the term number in the sequence 5, 10, 15... that is equal to 275, we can observe that each term is obtained by adding 5 to the previous term. So, it is an arithmetic sequence with a common difference of 5.
We can use the formula for the nth term of an arithmetic sequence to find the term number:
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, the first term (a1) is 5, the term number (n) is unknown, and the common difference (d) is 5. The value that we are looking for is 275.
Setting up the equation:
275 = 5 + (n-1)5
Simplifying the equation:
275 = 5 + 5n - 5
275 = 5n
Dividing both sides by 5:
55 = n
Therefore, the term number in the sequence 5, 10, 15... that is equal to 275 is 55, not 1357.
To find the seventh term of an arithmetic sequence with a first term of -8 and a common difference of 3, we can use the same formula as before:
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, the first term (a1) is -8, the term number (n) is 7, and the common difference (d) is 3.
Therefore, the seventh term is calculated as follows:
a7 = -8 + (7-1)3
a7 = -8 + 6 * 3
a7 = -8 + 18
a7 = 10
Yes, the seventh term of the arithmetic sequence with a first term of -8 and a common difference of 3 is indeed 10.
To find the nth term of an arithmetic sequence, you can use the formula an = a1 + (n-1)d, where an represents the nth term, a1 is the first term, n is the term number, and d is the common difference.
Let's apply this formula to each of the given questions:
1. For the sequence -6, 1, 8..., to find the 10th term:
a1 = -6 (first term), d = 1 - (-6) = 7 (common difference), n = 10 (10th term)
Using the formula, an = a1 + (n-1)d:
a10 = -6 + (10-1)7
a10 = -6 + 63
a10 = 57
Therefore, the 10th term of the sequence -6, 1, 8... is indeed 57.
2. For the sequence 2, 4, 8, 16, to find the value of s4:
s4 refers to the sum of the first four terms of the sequence.
Using the formula for the sum of an arithmetic series, Sn = (n/2)(a1 + an):
a1 = 2, an = 16, n = 4
s4 = (4/2)(2 + 16)
s4 = 2(18)
s4 = 36
Therefore, the value of s4 for the sequence 2, 4, 8, 16 is indeed 36.
3. For the sequence 1, 2, 4..., to find the 7th term:
a1 = 1, d = 2 - 1 = 1, n = 7
Using the formula, an = a1 + (n-1)d:
a7 = 1 + (7-1)1
a7 = 1 + 6
a7 = 7
Therefore, the 7th term of the sequence 1, 2, 4... is indeed 7.
4. For the sequence 5, 10, 15..., to find which term is 275:
a1 = 5, d = 10 - 5 = 5
We need to find the value of n in the formula an = a1 + (n-1)d:
275 = 5 + (n-1)(5)
275 = 5 + 5n - 5
275 = 5n
n = 275/5
n = 55
Therefore, the term number 55 corresponds to the value 275 in the sequence 5, 10, 15...
5. For an arithmetic sequence with a first term of -8 and a common difference of 3, to find the 7th term:
a1 = -8, d = 3, n = 7
Using the formula, an = a1 + (n-1)d:
a7 = -8 + (7-1)3
a7 = -8 + 18
a7 = 10
Therefore, the 7th term of the arithmetic sequence with a first term of -8 and a common difference of 3 is indeed 10.