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 answer:

n =  7

Step-by-step explanation:

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 will be pleased if You send us any improvements to this math problem. Thank you!






avatar




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

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

Related math problems and questions:

  • 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:
  • 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?
  • Sequence
    sunflower Between numbers 1 and 53 insert n members of the arithmetic sequence that its sum is 702.
  • Find the sum
    arithmet_seq_2 Find the sum of all natural numbers from 1 and 100, which are divisible by 2 or 5
  • 1200 screws
    matica 1200 screws are to be divided into 3 groups so that in the 1st group there are 300 screws more than in the 2nd group and in the 2nd group 150 screws less than in the 3rd group. How many screws will be in each group?
  • Sequence 2
    seq2 Write the first 5 members of an arithmetic sequence a11=-14, d=-1
  • Sequence 11
    sequence_geo_2 What is the nth term of this sequence 1, 1/2, 1/3, 1/4, 1/5?
  • 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.
  • 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?
  • 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.
  • Consecutive numbers
    progression Sum of ten consecutive numbers is 105. Determine these numbers (write first and last).
  • Cuboid walls
    cuboid_9 Calculate the cuboid volume if its different walls have an area of 195cm², 135cm², and 117cm².
  • 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
    arithmetic_seq In the arithmetic sequence is a1=-1, d=4. Which member is equal to the number 203?
  • Adding
    eq1 Divide number 135 into two additions so that one adds 30 more than 2/5 of the other add. Write the bigger one.