Question

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

Answer 1

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

Explanation:

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

`T_n=3n+17`

Subtract 17 from both the sides.

`T_n-17=3n`

Divide both sides by 3.

`(T_n-17)/(3)=n`

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

(a) The given term is 80.

`n=(80-17)/(3)=21`

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

(b) The given term is 170.

`n=(170-17)/(3)=51`

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

(c) The given term is 217.

`n=(217-17)/(3)=66.67`

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

(d) The given term is 312.

`n=(312-17)/(3)=98.33`

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

(e) The given term is 278.

`n=(278-17)/(3)=87`

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

(f) The given term is 3566.

`n=(3566-17)/(3)=1183`

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

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