Question

1.5, 2, 2.5, 3, 3.5
Work out the nth term

Answer 1

Answer: n = 0.5n + 1

Step-by-step explanation:

The 1st term starts with 1.5 and the 2nd is 2. So you have to start with 0.5 and 1 since there is no such thing as a 0th term; you have to split 1.5 at the start.

Answer 2

Answer: 0.5n + 1

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Step-by-step explanation:

The starting term is
`a_1 = 1.5` and the common difference is d = 0.5

If we have an arithmetic sequence, then,

`a_n = a_1 + d(n-1)\\\\a_n = 1.5 + 0.5(n-1)\\\\a_n = 1.5 + 0.5n-0.5\\\\a_n = 0.5n + 1\\\\`

represents the nth term.

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To partially check the answer, let's try n = 3

`a_n = 0.5n + 1\\\\a_3 = 0.5(3) + 1\\\\a_3 = 1.5 + 1\\\\a_3 = 2.5\\\\`

The third term is indeed 2.5, so we have confirmed the nth term formula works for n = 3. I'll let you try out the other values of n.