Find n for a series for which a1= 30, d = -4, and sn = -210. a. -21 b. 21 c. -10 d. 10 select the best answer from the choices provided a) a b) b c) c d) d

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

a1= 30 and d= -4 sn =-210

Plug in the values and solve for n

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

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

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