Answer: 17+3(n-1)
This simplifies to 3n+14
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Explanation:
[tex]a_1 = 17[/tex] is the first term
[tex]d = 3[/tex] is the common difference, or the gap between terms. Eg: the jump from 17 to 20 is +3.
This means the nth term is...
[tex]a_n = a_1 + d(n-1)\\\\a_n = 17+3(n-1)\\\\a_n = 17 + 3n-3\\\\a_n = 3n+14[/tex]
As a check, if we tried something like n = 2, then,
[tex]a_n = 3n+14\\\\a_2 = 3*2+14\\\\a_2 = 20[/tex]
which matches with the second term of the sequence your teacher gave you. I'll let you check the other terms.
