Common difference

The 4th term of an arithmetic progression is 6. If the sum of the 8th and 9th term is -72, find the common difference.

Correct result:

d =  -9.3333

Solution:

a4=6 a8+a9=72 (a4+4d)+(a4+5d)=72  2a4+9d=72  d=(722 a4)/9=(722 6)/9=283=9139.3333=9.3333   Verifying Solution:  a1=a43 d=63 (9.3333)=34 k8=a1+7 d=34+7 (9.3333)=943=311331.3333 k9=a1+8 d=34+8 (9.3333)=1223=402340.6667 s89=k8+k9=(31.3333)+(40.6667)=72



We would be pleased if you find an error in the word problem or inaccuracies and send it to us. Thank you!



Showing 0 comments:
avatar




You need to know the following knowledge to solve this word math problem:

Related math problems and questions:

  • Arithmetic progression 2
    seq_sum The 3rd term of an Arithmetic progression is 10 more than the first term while the fifth term is 15 more than the second term. Find the sum of the 8th and 15th terms of the Arithmetic progression if the 7th term is 7 times the first term.
  • If the 3
    sequence_geo If the 6th term of a GP is 4 and the 10th is 4/81, find common ratio r.
  • In the 8
    seq In the A. P. 36, 39, 42, …, which term is 276?
  • What is 10
    numbers2_4 What is the 5th term, if the 8th term is 80 and common ratio r =1/2?
  • Geometric progressiob
    eq2 If the sum of four consective terms of geometric progression is 80 and arithmetic mean of second and fourth term is 30 then find terms?
  • Fifth member
    arithmet_seq_1 Determine the fifth member of the arithmetic progression, if the sum of the second and fifth members equal to 73, and difference d = 7.
  • Difference AP
    delta Calculate the difference of arithmetic progression if the sum of its first 19 members Sn = 8075 and the first member is a1 = 20
  • Negative difference
    arithmet_seq Find four arithmetic progression members between 7 and -6.
  • HP - harmonic progression
    sequence_geo_1 Determine the 8th term of the harmonic progression 2, 4/3, 1,…
  • HP - harmonic progression 2
    seq Compute the 16th term of the HP if the 6th and 11th term of the harmonic progression are 10 and 18 respectively.
  • Determine AP
    diff Determine the difference of the arithmetic progression if a3 = 7, and a4 + a5 = 71
  • AS sequence
    AP In an arithmetic sequence is given the difference d = -3 and a71 = 455. a) Determine the value of a62 b) Determine the sum of 71 members.
  • Sum 1-6
    seq_sum Find the sum of the geometric progression 3, 15, 75,… to six terms.
  • Find the 19
    numbers_3 Find the 1st term of the GP ___, -6, 18, -54.
  • Angles of a hexagon
    hexagon-irregular Find the interior angles of a hexagon if the sizes of the angles form an arithmetic sequence and the smallest angle is 70°.
  • Sum of the seventeen numbers
    seq_sum The sum of the 17 different natural numbers is 154. Determine the sum of the two largest ones.
  • GP - three members
    progression_ao The second and third of a geometric progression are 24 and 12(c+1) respectively, given that the sum of the first three terms of progression is 76 determine value of c