Find the sum

Question

The number of cranes born each year in a new aviary forms a
sequence whose general term is an = n² + 2n - 1. Find the
number of cranes born in the fourth year and the total number
of cranes born in the first four years.

Answer 1

For the first year n = 1

n = 2, second year

n = 3, third year

and n  =4, represents the fourth year

 

Given: a_n = n² + 2n - 1

 

For n = 1

a₁ = 1² + 2(1) - 1 = 2

 

For n = 2

a₂ = 2² + 2(2) - 1 = 7

 

for n = 3

a₃ = 3² + 2(3) - 1 = 14

 

for n = 4

a₄ = 4² + 2(4) - 1 = 23

 

 

n = 4 represents the number born in the fourth year is a₄ = 23

 

The total number born in the first four years is:

S = a₁ + a₂ + a₃ +a₄ = 2 + 7 + 14 + 23 = 46

S = 46