Answered

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

Sagot :

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.

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