arithmetic

posted by .

The first term of a quadratic sequence is 8 and it's fourth is 32. If the second difference of the sequence is 2, find Tn.

  • arithmetic -

    the general term of a quadratic sequence is
    term(n) = an^2 + bn + c, where a, b, and c are constants
    It can be shown using differences that a is (1/2) of the second difference.
    Thus a = 1
    so term(1) = 8
    8 = 1(1^2) + b(1) + c ---> b+c = 7
    term(4) = 32
    32 = 1(2^2) + b(2) + c ---> 2b + c = 28

    subtract them: b = 21
    then c = 7-21 = -14

    term(n) = n^2 + 21n - 14

  • correction - arithmetic -

    I used the 32 as if it were the 2nd terms, should have been the 4th

    Here is the correct version


    Thus a = 1
    so term(1) = 8
    8 = 1(1^2) + b(1) + c ---> b+c = 7
    term(4) = 32
    32 = 1(4^2) + b(4) + c ---> 4b + c = 16

    subtract them:
    3b = 9
    b = 3

    then c = 7-3 = 4

    term(n) = n^2 + 3n + 4


    check:
    t(1) = 1+3+4 = 8
    t(4) = 16 + 12 + 4 = 32

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Mathematics : Arithmetic Sequence

    The 5th term and the 8th term of an arithmetic sequence are 18 and 27 respctively. a)Find the 1st term and the common difference of the arithmetic sequence. b)Find the general term of the arithmetic sequence.
  2. Math

    A sequence is formed by adding together the corresponding terms of a geometric sequence and and an arithmetic sequence.The common ratio of the geometric sequence is 2 and the common difference of the arithmetic sequence is 2.The first …
  3. Arithmetic Sequence

    Given the third term of an arithmetic sequence less than the fourth term by three. The seventh term is two times the fifth term. Find the common difference and the first term.
  4. 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 …
  5. Algebra

    True or False 1. – 5, – 5, – 5, – 5, – 5, … is an arithmetic sequence. 2. In an arithmetic sequence, it is possible that the 13th term is equal to its 53rd term. 3. In an arithmetic sequence, the common difference is computed …
  6. arithmetic sequence

    the 40th term of an arithmetic sequence is equal to the sum of the 20th and 31st term. if the common difference of the sequence is-10. find the first term.
  7. Algebra

    I am so lost on these problems. Write a geometric sequence that starts with 3 and has a common ratio of 5. What is the 23rd term in the sequence. Write an arithmetic sequence that has a common difference of 4 and the eighth term is …
  8. Quick math help

    Find the tenth term of the sequence: -6,1,8... Is it 57?
  9. Quick Math Help

    Find the tenth term of the sequence: -6,1,8... Is it 57?
  10. Quick math help

    Find the tenth term of the sequence: -6,1,8... Is it 57?

More Similar Questions