Question

Write the first five terms in the sequence defined by the explicit formula an=n2-2

Answer 1

`a_n=n^2-n\\\\\text{Put}\ n=1,\ n=2,\ n=3,\ n=4,\ n=5\ \text{to the equation}.\\\\n=1\to a_1=1^2-1=1-1=0\\\\n=2\to a_2=2^2-2=4-2=2\\\\n=3\to a_3=3^2-3=9-3=6\\\\n=4\to a_4=4^2-4=16-4=12\\\\n=5\to a_5=5^2-5=25-5=20\\\\Answer:\ \boxed{0,\ 2,\ 6,\ 12,\ 20}`

Answer 2

Answer: -1, 2, 7, 14, 23

Explanation:

aₙ = n² - 2

for n=1

a₁ = 1² - 2 = 1-2= -1

for n=2

a₂ = 2² - 2 = 4-2 =2

for n= 3

a₃ =3² - 2 = 9-2=7

for n=4

a₄= 4² - 2 = 16-2=14

for n=5

a₅= 5² - 2=25-2=23

Therefore, the first five terms of the sequence are; -1, 2, 7, 14 and 23