maths

posted by .

Consider the sequence
1,-2, 3,-4, 5, -6,.........., n(-1)^(n+1)

What is the average of first 300 terms of the sequence?

  • maths -

    rearrange the terms to see that the first 2n terms are
    1+3+5+... - 2(1+2+3+...)
    = n^2 - 2(n(n+1)/2)
    = n^2 - n^2-n
    = -n
    so, the average is -n/2n = -1/2

    or, rearrange to see that the first 2n terms are
    (1-2)+(3-4)+...+(n-(n+1))
    = -1 + -1 + ...
    = -n
    average is -n/2n = -1/2

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. maths

    consider the sequence given by U1=-0.3 Un+1=Un+0.7 i)state what type of sequence this is. ii)write down the first 4 terms of the sequence. iii) find a closed form for sequnce. iv) use the closed form to find the nth term of the sequnce …
  2. Maths

    The first term of an arithmetic sequence is 2. The first, third and eleventh terms are the first three terms of a geometric sequence. Determine the seventh term of the geometric sequence
  3. Can someone help me?!

    The 1st, 5th and 13th terms of an arithmetic sequence are the first three terms of a geometric sequence with a common ratio 2. If the 21st term of the arithmetic sequence is 72, calculate the sum of the first 10 terms of the geometric …
  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. Math for Educators

    The first difference of a sequence is 8, 12, 16, 20,... The sum of the first two terms of the original sequence is 14. Find the first three terms of the original sequence. The first term of the original sequence is?
  6. 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 …
  7. MATH

    A new sequence is formed by adding together the corresponding terms of a geometric sequence and an arithmetric sequence. the geometric sequence has a common ratio of 3 and the arthmetric sequence has a common difference of -2. The …
  8. Maths

    In the sequence 3,p,q,24 are the first four terms.determine the values of p and q if the ,(a)the sequence is geometric .(b)the sequence is arithemetic
  9. maths

    the sum of the first nine terms of an arithmetic sequence 216. The 1st, 3rd and 7th terms form the first three terms of a geometric sequence therefore find the common difference
  10. math

    The first and second terms of an exponential sequence (G.P) are respectively the first and third terms of a linear sequence (A.P). The fourth term of the linear sequence is 10 and sum of its first five terms is 60. find (a) the first …

More Similar Questions