2. which of the following are terms of the series with nth term t-3n +17? a) 80 b) 170 c)217 d) 312 e) 278 f) 3566

The correct options are a,b,e and f.

Step-by-step explanation:

It is given that the nth terms of the series is defined as

Subtract 17 from both the sides.

Divide both sides by 3.

The term Tₙ is a term of given series if n is a positive integer.

(a) The given term is 80.

Since n is a positive integer, therefore 80 is a term of given series.

(b) The given term is 170.

Since n is a positive integer, therefore 170 is a term of given series.

(c) The given term is 217.

Since n is not a positive integer, therefore 217 is a term of given series.

(d) The given term is 312.

Since n is not a positive integer, therefore 312 is a term of given series.

(e) The given term is 278.

Since n is a positive integer, therefore 278 is a term of given series.

(f) The given term is 3566.

Since n is a positive integer, therefore 3566 is a term of given series.

Thus, the correct options are a, b, e and f.

i believe the answer is the polygon, heptagon.

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