What is the sum of a 44 term arithmetic sequence where the first term is -9 and the last term is 120

2442

Step-by-step explanation:

The n th term of an arithmetic sequence is

= a₁ + (n - 1)d

where a₁ is the first term and d is the common difference

We require to find d knowing that 120 is the 44 th term, thus

= - 9 + 43d = 120 ( add 9 to both sides )

43d = 129 ( divide both sides by 43 )

d = 3

The sum to n terms of an arithmetic sequence is

= [ 2a₁ + (n - 1)d ], hence

= [ (2 × - 9 + (43 × 3) ]

                          = 22(- 18 + 129)

                          = 22 × 111 = 2442

OR

Since the first and last terms in the sequence are known, then

= ( first + last )

= 22(- 9 + 120) = 22 × 111 = 2442

step-by-step explanation: