math

Find the exact value (either decimal or fractional form) of the first term of an arithmetic sequence if the sum of the first 100 terms is 7099.5 and the sum of the next 100 terms is 20799.

  1. 👍
  2. 👎
  3. 👁
  1. We find a from a system:
    a +a+99d =7099.5
    a+100d+a+199d=20799

    We subtract from the 2nd the 1st:

    200d=13699.5
    d=68.4975

    2a+99x68.4975=7099.5
    a=159.12375 (0.12375=99/800)

    1. 👍
    2. 👎
  2. Ummm.

    Sn = n(a1 + an)/2
    S100 = 100(a1 + a100)/2
    = 50(a+a+99d)
    = 100a + 4950

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    Determine whether each sequence is arithmetic or geometric. Find the next three terms. 1. 14, 19, 24, 29, . . . (1 point) geometric, 34, 39, 44 arithmetic, 32, 36, 41 arithmetic, 34, 39, 44 *** The sequence is neither geometric

  2. Mathematics

    In an arithmetic sequence the sum of the first ten terms is 400 and the sum of next ten terms is 1000. Find The common difference The first term The first three terms of arithmetic sequence are also 2x, x+4 and 2x-7. Verify that

  3. Math

    The first term and last term of an arithmetic progression are -4 and 145 respectively. If the common difference is 4. (a) find the 12th term (b) find the 25th term.

  4. Math

    The 9th term of an arithmetic progression is three times the 5th term, find the relationship between the first term and common difference

  1. Utech

    The 9th term of an Arithmetic Progression is 8 and the 4th term is 20. Find the first term and the common difference.

  2. Math,science

    The 5th term of an arithmetic progression is 23 and the 12th term is 37.find the third term and common different

  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. algebra

    1)Find the 20th term of the arithmetic sequence in which a1=3 and d=7 a.143 b.136 c.140 d.133 an=a1+(n-1)d a20=3+(20-1)7 a20=3+(19)7 a20=3+133 answer=b 2)Write an equation for the nth term of the arithmetic sequence -3,3,9,15...

  1. math

    Find the arithmetic sequence whose fifth term = 21, and the tenth term = 3 times the second term

  2. Mathematics

    The 10th term of an arithmetic progression is _27 and 5th term is _12 ,what is the 18th term ?find also the sum of its 25 term

  3. Math

    The fourth term of an arithmetic sequence is less than the fifth term by 3. The seventh term is three times the fifth term. Find the common difference and the first term

  4. Math.

    The 4th term of the arithmetic progression is15 and the9th term is 35 find the 15th term.

You can view more similar questions or ask a new question.