Question

I WILL GIVE BRAINLIEST AND 5 STARS TO CORRECT ANSWER AND IF YOU SHOW YOUR WORK

Answer 1

The formula for an arithmetic sequence is An=A1+(n-1)d. 
Using this knowledge, you can set up the equation easily to be An=1+(12-1)-5
You then simplify this to 1-55 using PEMDAS, giving you the answer for the twelfth term being -54, you then do this for every term if you want (or you could just subtract 5 by the terms after 14 till you get to -54. After all that, you add the twelve terms up to get -319 as your final answer

Answer 2

We see that:

$a_2-a_1=-4-1=\boxed{-5}\\\\ a_3-a_2=-9-(-4)=-9+4=\boxed{-5}\\\\ a_4-a_3=-14-(-9)=-14+9=\boxed{-5}\\\\\ldots$

So this is an arithmetic sequence with common difference d = -5. We can calculate the sum of that sequence as:


Sum = (first term + last term) * number of terms/2

first term = 1
number of terms = 12

last term = a₁₂ = ?

We know that:

$a_{n} = a_1+(n-1)\cdot d$

so:

$a_{12}=a_1+(12-1)\cdot d=1+11\cdot(-5)=1-55=\boxed{-54}$

And sum:

$S_{n}=(a_1+a_{n})\cdot\frac{n}{2}\\\\\\ S_{12}=\big(1+(-54)\big)\cdot\frac{12}{2}\\\\\\ S_{12}=-53\cdot6\\\\\\\boxed{S_{12}=-318}$