The first term of Arithemetic sequence is -7 and common difference is 3 find five six terms and determine first 50 terms of sequence

Answer 1

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.