The first term of Arithemetic sequence is -7 and common difference is 3 find five six terms and determine first 50 terms of sequence
To find the fifth term of the arithmetic sequence, we can use the formula:
\[a_n = a_1 + (n-1)d\]
where \(a_n\) is the \(n\)th term, \(a_1\) is the first term, \(d\) is the common difference, and \(n\) is the position of the term.
Using the given values, we have:
\[a_5 = -7 + (5-1)(3) = -7 + 4(3) = -7 + 12 = 5\]
Therefore, the fifth term of the arithmetic sequence is 5.
To find the sixth term, we can use the same formula:
\[a_6 = -7 + (6-1)(3) = -7 + 5(3) = -7 + 15 = 8\]
Therefore, the sixth term of the arithmetic sequence is 8.
To determine the first 50 terms of the sequence, we can list out the terms using the given information.
The first term is -7, and the common difference is 3. Therefore, we can write out the sequence as follows:
\[a_1 = -7\]
\[a_2 = -7 + 3 = -4\]
\[a_3 = -7 + 2(3) = -1\]
\[a_4 = -7 + 3(3) = 2\]
\[a_5 = -7 + 4(3) = 5\]
\[a_6 = -7 + 5(3) = 8\]
\[...\]
\[a_{50} = -7 + 49(3) = 140\]
Therefore, the first 50 terms of the arithmetic sequence are:
-7, -4, -1, 2, 5, 8, ..., 140.
To find the terms of an arithmetic sequence, we can use the formula:
nth term = first term + (n -1) * common difference
Given that the first term is -7 and the common difference is 3, let's find the first six terms:
1st term = -7 + (1 - 1) * 3 = -7 + 0 = -7
2nd term = -7 + (2 - 1) * 3 = -7 + 3 = -4
3rd term = -7 + (3 - 1) * 3 = -7 + 6 = -1
4th term = -7 + (4 - 1) * 3 = -7 + 9 = 2
5th term = -7 + (5 - 1) * 3 = -7 + 12 = 5
6th term = -7 + (6 - 1) * 3 = -7 + 15 = 8
Therefore, the first six terms of the sequence are: -7, -4, -1, 2, 5, 8.
To determine the first 50 terms of the sequence, we can use the same formula:
nth term = -7 + (n - 1) * 3
Let's find the first 50 terms using this formula:
1st term = -7 + (1 - 1) * 3 = -7 + 0 = -7
2nd term = -7 + (2 - 1) * 3 = -7 + 3 = -4
3rd term = -7 + (3 - 1) * 3 = -7 + 6 = -1
4th term = -7 + (4 - 1) * 3 = -7 + 9 = 2
...
50th term = -7 + (50 - 1) * 3 = -7 + 147 = 140
Therefore, the first 50 terms of the sequence are: -7, -4, -1, 2, 5, 8, ..., 140.