Find the sum of the first 12 terms of the sequence. 1, -4, -9, -14, . . . What is the formula that I need to use?

Question

What is the formula that I need to use? The asnwer is obviously -54. 

Answer 1

The first 12 terms are:

  1   -4   -9   -14   -19   -24   -29   -34   -39   -44   -49   -54

 

This is an Arithmetic Sequence.  The common difference, d, is (-5).  The first term, a₁, is 1.

 

Each term can be found using the formula:

     a_n = a₁ + (n-1)d

 

 

The sum of the first n terms can be found using the formula:

    S_n = (n/2)(a₁ + a_n)

For this problem:

    S₁₂ = (12/2)(1 + (-54))

    S₁₂ = -318

Answer 2

1, -4, -9, -14,

 

this is arithmetic sequence

with difference =d = -5

 

a₁₂ = a₁ +(n-1) d

 

      =1 +(12-1)(-5)

 

      = 1+(11)(-5)

 

      = 1 -55

 

      = -54

 

 

  sum of the first 12 terms =( n/2 ) * (a₁ +a₁₂)

 

                                       =12/2 (1-54)

                            

                                       =6(-53)

                             

                                        =-318