Answer:
n= 21 option B
Step-by-step explanation:
a1= 30, d = -4, and Sn = -210
WE use sum formula
we are given with a1 and d so its arithmetic sequence
the sum formula for arithmetic sequence is
[tex]S_n = \frac{n}{2}(2a_1 +(n-1)d)[/tex]
a1= 30 and d= -4 sn =-210
Plug in the values and solve for n
[tex]-210= \frac{n}{2}(2(30) +(n-1)(-4))[/tex]
[tex]-210= \frac{n}{2}(60-4n+4)[/tex]
[tex]-210= \frac{n}{2}(64-4n)[/tex]
Now distribute the fraction n/2
-210 = 32n - 2n^2
we add 210 on both sides
-2n^2 +32n +210=0
Divide whole equation by -2
[tex]n^2 - 16n - 105=0[/tex]
Now we factor left hand side
Product is -105 and sum is -16
-21 times (5) = -105
-21 + (5) = -16
(n-21) (n+5)=0
n -21 = 0 so n= 21
n +5 =0 so n = -5
number of terms cannot be negative so n= 21
