math sequences and series

posted by .

how do i solve the sum of the first two terms of an arithmetic sequence is 16. the sum of the second and third term is 28. determine the first three terms, algebraically

  • math sequences and series -

    a1 + a2 = 16

    a2 + a3 = 28

    and since it is an arithmetic sequence
    a2 - a1 = a3 - a2
    or
    a2 = (a1+a3)/2 (the average of course)

    substitute back
    a1 + (a1+a3)/2 = 16
    (a1+a3)/2 + a3 = 28

    solve those two equations for a1 and a3, then go back and get a2

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Precalculus

    The 8th term in an arithmetic sequence is 5, and the sum of the first 10 terms is 20. Find the common difference and the first term of the sequence. Alright so in an arithmetic squence the difference d between any two successive numbers …
  2. sequences and series

    how do i solve the sum of the first two terms of an arithmetic sequence is 16. the sum of the second and third term is 28. determine the first three terms, algebraically
  3. Further mathematics

    An exponential sequence of positive terms and a linear sequence have the same first term.the sum of their first terms is 3 the sum of their second terms is 3/2,and the sum of their third terms is 6.find their fifth terms.
  4. Math *URGENT

    Please give the answers and solutions for each. 1.If the second term is 2 and the seventh term of a geometric sequence is 64, find the 12th term. 2. Which term if the geometric sequence 18,54,162,486,... is 3,188,646?
  5. Maths

    An arithmetic and a geometric sequence have the same first terms.(2)....and the same second term say X..The sum of the first 3 terms of the arithmetic sequence equals to the third term of the geometric sequence.Calculate the first …
  6. Maths

    1..The first 2 terms of a geometric progression are the same as the first two terms of an arithmetic progression.The first term is 12 and is greater than the second term.The sum of the first 3 terms od the arithmetic progression is …
  7. Math(arithmetic & Geometric Series)

    1)The sum of 6 terms of an arithmetic series is 45, the sum of 12 terms is -8. Find the first term and the common difference?
  8. Further mathematics

    An exponential sequence (GP)of positive terms and a linear sequence (AP)have the same first term.the sum of their first terms is 3,the sum of their second terms is 3 and the sum of their third terms is 6. Find the sum of their fifth …
  9. Mathematics arithmetic sequence

    The sum of second and sixth terms of an arithmetic sequence is 4. The third term is 24 more than eleventh term. So determine the first three terms of the sequence.
  10. math

    in an arithmetic sequence the common difference is equal to 2.the first term is also the first term of a geometric sequence. the sum of the first 3 terms of an arithmetic sequence and the sum of the first 9 terms of an arithmetic sequence …

More Similar Questions