The 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?

Correct answer:

s2 =  30

Step-by-step explanation:

s1=120 n=10  s1=a1+a2+a3+…+an  d2=d1−2  s1=10/2⋅ (a1+a1+9⋅ d1)=10⋅ a1+45⋅ d1=120 s2=10/2⋅ [a1+a1+9⋅ (d1−2)] s2=10⋅ a1+45⋅ d1−5⋅ 9⋅ 2  s2=s1−5⋅ 9⋅ 2=120−5⋅ 9⋅ 2=30

Try another example


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






avatar




Tips to related online calculators
Looking for help with calculating arithmetic mean?
Looking for a statistical calculator?

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


 
We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions:

  • Finite arithmetic sequence
    seq_sum_1 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?
  • 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
  • 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
    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).
  • 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 the seventeen numbers
    seq_sum The sum of the 17 different natural numbers is 154. Determine the sum of the two largest ones.
  • AP - simple
    progression_1 Find the first ten members of the sequence if a11 = 132, d = 3.
  • AS - sequence
    matematika_icon What are the first ten members of the sequence if a11=22, d=2.
  • Find the sum
    arithmet_seq_2 Find the sum of all natural numbers from 1 and 100, which are divisible by 2 or 5
  • Sequence 3
    75 Write the first 5 members of an arithmetic sequence: a4=-35, a11=-105.
  • Sequences AP + GP
    seq_sum The three numbers that make up the arithmetic sequence have the sum of 30. If we subtract from the first 5, from the second 4 and keep the third, we get the geometric sequence. Find AP and GP members.
  • 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 members
    seq_5 What is the sum of the first two members of the aritmetic progression if d = -4.3 and a3 = 7.5?
  • No. 215
    215_num From the number 215 we can create a four-digit number that among its numbers manually type any other digit. Thus, we created two four-digit numbers whose difference is 120. What two four-digit numbers that might be?
  • Sum of odd numbers
    seq_sum Find the sum of all odd integers from 13 to 781.
  • Negative difference
    arithmet_seq Find four arithmetic progression members between 7 and -6.