The sum of consecutive integers 1,2,3,..., n is given by the formula 1/2n(n+1)

Question

The sum of consecutive integers 1,2,3,..., n is given by the formula 1/2n(n+1). HOw many consecutive integers, starting with 1, must be added to get a sum of 1176? 

 

a) definition of variables 

b and c) Equation and solution process

d) Solution in sentence form with units:

Answer 1

S_n = n/2(a₁ + a₁ + (n - 1)d), where n = number of terms, d = common difference, a₁ = first term

S_n = n/2(2a₁ + n - 1)

S_n = n/2(2 + n - 1)

S_n = n/2(n + 1)

 

1176 = n/2(n + 1)                Multiply both sides by 2

2351 = n(n + 1)

2351 = n² + n

0 = n² + n - 2351

0 = (n + 49)(n - 48)

 

The sum of 48 integers is 1176.