Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

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

Sagot :

really226

Answer:

- 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

Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.