Answer:
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.