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2. Which of the following are terms of the series with nth term [tex]T_n = 3n + 17[/tex]?

A. 80
B. 170
C. 217
D. 312
E. 278
F. 3566

Answer :

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

[tex]T_n=3n+17[/tex]

Subtract 17 from both the sides.

[tex]T_n-17=3n[/tex]

Divide both sides by 3.

[tex]\frac{T_n-17}{3}=n[/tex]

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

(a) The given term is 80.

[tex]n=\frac{80-17}{3}=21[/tex]

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

(b) The given term is 170.

[tex]n=\frac{170-17}{3}=51[/tex]

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

(c) The given term is 217.

[tex]n=\frac{217-17}{3}=66.67[/tex]

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

(d) The given term is 312.

[tex]n=\frac{312-17}{3}=98.33[/tex]

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

(e) The given term is 278.

[tex]n=\frac{278-17}{3}=87[/tex]

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

(f) The given term is 3566.

[tex]n=\frac{3566-17}{3}=1183[/tex]

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

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

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