Find the sum of the first 12 terms of the sequence. Show all work for full credit.

1, -4, -9, -14, . . .

please this is my last question and i cant seem to get it right. if possible can someone work it out for me?

Question

Find the sum of the first 12 terms of the sequence. Show all work for full credit.

1, -4, -9, -14, . . .

please this is my last question and i cant seem to get it right. if possible can someone work it out for me?

campbell_st · Answer

what do you know about the question..?

anonymous · Answer

i believe its an arithmetic sequence?

campbell_st · Answer

good start, what's the common difference..?

anonymous · Answer

ok that where i confuse myself

campbell_st · Answer

well what is the sequence changing by... 

common difference = 2nd term - 1st term 

check with   3rd term - 2nd term.... is it the same

anonymous · Answer

-5

campbell_st · Answer

great... and the 1st term a = 1 

so for  the sum of the sequence you can use the formula 

$$S_{n} = \frac{n}{2}[2a + (n - 1) \times d]$$

you are given a = 1, you found d = -5 and have been told n = 12 

so substitute them and calculate the sum

anonymous · Answer

i get the plugging in but what does d equal? all the rest i plugged in

campbell_st · Answer

d is the common difference d = -5

anonymous · Answer

i see ok 1 min

anonymous · Answer

is it 6/-53

anonymous · Answer

that's what i got but I not entirely sure.

campbell_st · Answer

you are close the calculation becomes 

$$S_{12} = \frac{12}{2} \times (-53)$$

campbell_st · Answer

so then 

$$S_{12} = 6 \times (-53)$$

anonymous · Answer

so that is the final form?