Question

Find the sum of the first 12 terms of the sequence. Show all work for full credit. 1, -4, -9, -14, . . .

Answer 1

find the common difference, subtract the first term from the second term.
-4 - 1 = -5....so the common difference is -5.

now we will find the 12th term...we need to know this in order to find the sum.
an = a1 + (n-1) * d
n = term we want to find = 12
a1 = first term = 1
d = common difference = -5
now we sub
a12 = 1 + (12 - 1) * -5
a12 = 1 + 11 * -5
a12 = 1 - 55
a12 = - 54

now we use the sum formula
sn = (n(a1 + a12) / 2
s12 = 12 (1 - 54) / 2
s12 = 12(-53)/2
s12 = -636/2
s12 = - 318 <====

Answer 2

`a_1=1;\ a_2=-4;\ a_3=-9;\ a_4=-14;\ ...\\\\It's\ an\ arithmetic\ sequence.\\\\d=a_2-a_1\to d=-4-1=-5\\\\a_n=a_1+(n-1)d\to a_n=1+(n-1)(-5)=1-5n+5=6-5n\\\\S_n=(a_1+a_n)/(2)\cdot n\\\\a_(12)=6-5\cdot12=6-60=-54\\\\subtitute\\\\S_(12)=(1+(-54))/(2)\cdot12=(1-54)\cdot6=-53\cdot6=-318\\\\Answer:\boxed{-318}`