Question

Consider the sequence: The first term of an arithmetic sequence is 3 and its constant difference is 4. Is 95 a term in this sequence

Answer 1

Answer: Yes, 95 is a term in this sequence

Work Shown

`a_1 = 3 = \text{first term}\\d = 4 = \text{common difference}`

`a_n = \text{nth term of arithmetic sequence}\\\\a_n = a_1 + d(n-1)\\\\a_n = 3 + 4(n-1)\\\\a_n = 4n- 1`

Plug in
`a_n = 95` and solve for variable n.

`a_n = 4n- 1\\\\95 = 4n- 1\\\\95+1 = 4n\\\\96 = 4n\\\\n = 96/4\\\\n = 24`

This tells us that plugging n = 24 into
`a_n = 4n- 1` will lead to
`a_(24) = 95`

Meaning that the 24th term of this arithmetic sequence is 95.

Therefore, 95 is a term in this sequence.