MaTh

Let a_1, a_2, . . . , a_10 be an arithmetic sequence. If a_1 + a_3 + a_5 + a_7 + a_9 = 17 and a_2 + a_4 + a_6 + a_8 + a_{10} = 15, then find a_1.

  1. 👍 0
  2. 👎 0
  3. 👁 60
asked by Speedo
  1. 5/2 (a + a+4*2d) = 17
    5/2 (a+d + a+d+4*2d) = 15

    a=5, d = -2/5

    Check: The odd terms are
    5, 21/5, 17/5, 13/5, 9/5. Sum=17
    and I bet the evens add up as well.

    1. 👍 0
    2. 👎 0
    posted by Steve
  2. Stop Cheating!

    1. 👍 0
    2. 👎 0
    posted by AoPS

Respond to this Question

First Name

Your Response

Similar Questions

  1. Sequences

    For any sequence of real numbers A = {A_1, A_2, A_3, ... }, define *A to be the sequence {A_2 - A_1, A_3 - A_2, A_4 - A_3,..}. Suppose that all of the terms of the sequence *(*A) are 1, and that A_19 = A_92 = 0. Find A_1. Help me,

    asked by Joebelle on January 25, 2015
  2. Algebra

    the following problem refers to a geometric sequence: Find S_10 for -1, -1/3, -1/9 r=-1/3/-1=1/3 a_1=-1 a_2=-1/3 a_n=a_1*r^n-1 a_n=-1*1/3^n-1 s_n= Help me.

    asked by Keonn'a on September 28, 2018
  3. Algebra

    Find the sum of the infinite geometric series. 4+1+1/4+.... Sum=a_1/1-r 4/1-4=? r=a_1/a_2 r=4/1=4 a_1=4 I am stuck?Please help me.

    asked by Keonn'a on September 28, 2018
  4. math

    an = 3 a_{n-1} - 5 a_{n-2} - 4 a_{n-3} and a_4 = 42, a_5 = 147, and a_6 = 219. Find a_1, a_2, and a_3.

    asked by Denzel on November 29, 2013
  5. math

    The 3rd term in an arithmetic sequence is 12, the 7th term is 24, a) How many common differences are there between a_3 and a_7? b) What is the common difference of the sequence? c) What is the first term in the sequence? a_1 d)

    asked by edwin on May 21, 2014
  6. Algebra: please help me.

    The following problem refers to an arithmetic sequence. if a_8=9 and a_16=17, Find the term a_1, the common difference d, and then find a_30. a_n=a_1+(n-1)*d

    asked by Keonn'a on October 2, 2018
  7. Algebra

    What the general term a_n for the geometric sequence a_1= -5 and a_2= 15

    asked by Liz on September 2, 2012
  8. Algebra

    The following problem refers to a geometric sequence: If a_1=-2 and r=-1.Find s_28. This the formula was given by my instructor: S_n=a_1(1-r^n)/1-r =-2(1-(-1)^28)/1-(-1) =-2*2/2 =-4/2 =-2 where did I go wrong? Can You help me

    asked by Keonn'a on September 28, 2018
  9. Advanced Algebra

    The polynomial function defined by f(x) = 1 − x + x^2 − x^3 + ... + x^16 − x^17 may be written in the form f(y) = a_0 + a_1 y + a_2 y^2 + ... + a_16 y^16 + a_17 y^17, where y = x + 1 and a_i s are constants. Find a_2.

    asked by Frank on November 15, 2014
  10. Algebra

    The following problem refers to a geometric sequence. If a_1=-2 and r=-1. Find a_20. a_n=a_1*r^(n-1) a_20=-2*-1^(20-1) I am stuck now please help me.

    asked by Keonn'a on September 27, 2018

More Similar Questions