Question

What is the sum of a 30-term arithmetic sequence where the first term is 74 and the last term is -100?

a.-468

b.-442

c.-416

d.-390

Answer 1

The sum of 'n' terms of an arithmetic sequence is given by:\[\bf S_n=\frac{n}{2}(2a+(n-1)d)\]Where 'a' is the first term, 'n' is the term number of the nth term of the sequence and 'd' is the common difference.

Answer 2

Notice that we are given that there is 30-terms in this sequence hence \(\bf n=30\).
Also the first term is 74 and last term is -100 hence \(\bf a= 74\). But we still need to find the common difference \(\bf d\). To do this, we use the arithmetic sequence formula and we will solve for 'd':\[\bf a_n=a+(n-1)d \implies -100=74+(30-1)d\]Re-arranging yields:\[\bf d=\frac{ -100-74 }{ 29}=-6\]Now you have everything to calculate the sum. Plug the values in and solve.

@TeraByte

Answer 3

i got -390 :)

Answer 4

@genius12