Question

What are the first five terms of the sequence whose nth term is given by the formula a=n 2+1?

(A) 1, 2, 3, 4, 5
(B) 2, 5, 10, 17, 26
(C) 1, 3, 5, 7, 9
(D) 2, 4, 6, 8, 10

Answer 1

The first five terms of the sequence with the nth term formula a = n² + 1 are 2, 5, 10, 17, 26, which is option (B).

Step-by-step explanation:

The student has asked for the first five terms of the sequence whose nth term is given by the formula a = n² + 1. To find the first five terms, we simply substitute n = 1, 2, 3, 4, and 5 into the formula and calculate the respective terms. Here are the calculations:

• For n = 1: a1 = 1² + 1 = 1 + 1 = 2
• For n = 2: a2 = 2² + 1 = 4 + 1 = 5
• For n = 3: a3 = 3² + 1 = 9 + 1 = 10
• For n = 4: a4 = 4² + 1 = 16 + 1 = 17
• For n = 5: a5 = 5² + 1 = 25 + 1 = 26

Therefore, the first five terms of the sequence are 2, 5, 10, 17, 26, which corresponds to option (B).