determine the 1st term of the first 21 term of an arithmetic series if the sum of the three middle term is 126 and the sum of the three last terms is 288

- 18

Step-by-step explanation:

arithmetic  sequences are in form:

a(n)=a(o)+d(n-1)

sum are in form:

s(n)=[a(0)+a(n)](n/2)

three middle terms is:

10th, 11th, 12th term

How to think: 21 = 10+1+10 --> middle 3 is 10,11,12

sum of these 3 terms:

a(10)+a(11)+a(12)

=a(o)+9d+a(0)+10d+a(0)+11d

=3a(0)+30d=126

a(0)+10d=42 (equation 1)

Last three terms is:

19th, 20th, 21th

a(19)+a(20)+a(21)

=a(0)+18d+a(0)+19d+a(0)+20d

=3a(0)+57d=288

a(0)+19d=96 (equation 2)

now you have

a(0)+10d=42 (equation 1)

a(0)+19d=96 (equation 2)

solve and gives

d=6

a(0)= -18

10 glasses of juice could be made with 5 carrots, 1,500 orange juice, 2,000 papaya juice.

stew reads at the fastest rate of 265 words per minute.

step-by-step explanation:

it's a given that felicia reads at 260 word per minute and on connie's graph we can see that she reads 200 words per minute. since stew's table tells us that he read 795 in 3 minutes, we can divide 795 by 3 to find out how many words he reads per minute.

795/3 = 265

stew reads 265 words per minute - he reads at the fastest rate since felecia reads at 260 words per minute and connie reads at 200 words per minute.

stew (265) > felecia (260) > connie (200)