Question

Write the explicit formula for an, nth the term of the sequence 17,20,23

Answer 1

Answer:  17+3(n-1)

This simplifies to 3n+14

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Explanation:

$a_1 = 17$ is the first term

$d = 3$ is the common difference, or the gap between terms. Eg: the jump from 17 to 20 is +3.

This means the nth term is...

$a_n = a_1 + d(n-1)\\\\a_n = 17+3(n-1)\\\\a_n = 17 + 3n-3\\\\a_n = 3n+14$

As a check, if we tried something like n = 2, then,

$a_n = 3n+14\\\\a_2 = 3*2+14\\\\a_2 = 20$

which matches with the second term of the sequence your teacher gave you. I'll let you check the other terms.