Finite arithmetic sequence

How many numbers should be inserted between the numbers 1 and 25 so that all numbers create a finite arithmetic sequence and that the sum of all members of this group is 117?

Correct result:

n =  7


 x (1+25)/2=117  26x=234  x=9   n=x2=92=7   Verifying Solution:  a1=1 a9=25 d=a9a1n+1=2517+1=3 a2=a1+d=1+3=4 a3=a2+d=4+3=7 a4=a3+d=7+3=10 a5=a4+d=10+3=13 a6=a5+d=13+3=16 a7=a6+d=16+3=19 a8=a7+d=19+3=22   Verifying Solution:  b9=a8+d=22+3=25 b9=a9

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

Showing 0 comments:

Tips to related online calculators
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?

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

Next similar math problems:

  • 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.
  • The sum
    seq_sum The sum of the first 10 members of the arithmetic sequence is 120. What will be the sum if the difference is reduced by 2?
  • Statistics
    lines_globe The sum of all deviations from the arithmetic mean of the numerical sequence 4, 6, 51, 77, 90, 93, 95, 109, 113, 117 is:
  • The sum 6
    plusminus The sum of the 17 different natural numbers is 153. Determine the sum of the two largest ones.
  • Find the 21
    seq_sum Find the sum of the six terms of the finite geometric sequence 96, -48, 24, -12
  • Geometric progression
    exp_1 In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217.
  • Sequence
    sunflower Between numbers 1 and 53 insert n members of the arithmetic sequence that its sum is 702.
  • Geometric sequence 4
    Koch_Snowflake_Triangles It is given geometric sequence a3 = 7 and a12 = 3. Calculate s23 (= sum of the first 23 members of the sequence).
  • Numbers
    ten Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum?
  • Three members GP
    exp_growth The sum of three numbers in GP (geometric progression) is 21 and the sum of their squares is 189. Find the numbers.
  • Find the sum
    arithmet_seq_2 Find the sum of all natural numbers from 1 and 100, which are divisible by 2 or 5
  • Sum of members
    seq_5 What is the sum of the first two members of the aritmetic progression if d = -4.3 and a3 = 7.5?
  • Series
    fib Your task is express the sum of the following arithmetic series for n = 14: S(n) = 11 + 13 + 15 + 17 + ... + 2n+9 + 2n+11
  • Motel
    motorest Three different dinners A, B, C are served in the motel. Three 20 members went to motel. Group 1 ordered dinners: A 20 members and their average dinner price in the group was CZK 200. From Group 2, they ordered a A: 10 persons, B 10 dinners, and their ave
  • 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.
  • Sequence
    Quadratic_equation In the arithmetic sequence is given: Sn=2304, d=2, an=95 Calculate a1 and n.
  • Sequence 3
    75 Write the first 5 members of an arithmetic sequence: a4=-35, a11=-105.