The nth term of a sequence is 3n^2-1
a) find the second term of the sequence

b) find the fifth term of the sequence

Here, we are required to determine the second and fifth term of a sequence whose nth term is;

3n^2-1

The second term and fifth term of the sequence are;

(a) T(2nd) = 11

(b) T(5th) = 74

According to the question, the nth term is given as;

Nth = 3n² - 1.

Therefore, to find the second term, n= 2 is substituted for n in the expression.

Thus; T(2nd) = 3 (2)² - 1.

The second term of the sequence is, T(2nd) = 11

(b) Therefore, to find the second term, n= 5 is substituted for n in the expression.

Thus; T(5th) = 3 (5)² - 1.

The second term of the sequence is, T(5th) = 74

Ultimately, the 2nd and 5th term of the sequence are; 11 and 74 respectively.

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Step-by-step explanation:

To find the second and fifth terms substitute n = 2 and n = 5 into the rule, that is

(a)

= 3(2)² - 1 = (3 × 4) - 1 = 12 - 1 = 11

(b)

= 3(5)² - 1 = (3 × 25) - 1 = 75 - 1 = 74

Thus the second term is 11 and the fifth term is 74