Question

Write the first three terms in each of the sequence defined by the following :

(i) an​=3n+2
(ii) an​=n2+1

Answer 1

To find the terms of the sequences (i) an=3n+2, and (ii) an=n2+1, substitute the first three natural numbers for 'n'. The first three terms of sequence (i) are 5, 8, 11, and for sequence (ii) they are 2, 5, 10.

Step-by-step explanation:

The question asks to write the first three terms of two sequences defined by specific formulas. To find the terms of a sequence, you substitute the position number (n) into the given formula.

Sequence (i): an = 3n + 2

Substituting the first three position numbers (n=1, n=2, and n=3), we get:

• First term (n=1): a1 = 3(1) + 2 = 5
• Second term (n=2): a2 = 3(2) + 2 = 8
• Third term (n=3): a3 = 3(3) + 2 = 11

Sequence (ii): an = n2 + 1

Again, substituting the first three position numbers (n=1, n=2, and n=3), we find:

• First term (n=1): a1 = (1)2 + 1 = 2
• Second term (n=2): a2 = (2)2 + 1 = 5
• Third term (n=3): a3 = (3)2 + 1 = 10

So for sequence (i), the first three terms are 5, 8, and 11, while for sequence (ii), the first three terms are 2, 5, and 10.