Mathematics
Grade10
Easy

Question

What is the difference between the 20th term and 40th term of the Arithmetic Sequences with first term  5 and common difference 2?

  1. 20
  2. 40
  3. 50
  4. 110

hintHint:

The given question is about arithmetic progression. Arithmetic progression is a sequence of numbers where, the difference between two consecutive terms is constant. We are given the first term and the common difference. We are asked to find the difference between 20th and 40th term of the sequence.

The correct answer is: 40


    The first term of the progression is a= 5
    The common difference is d = 2
    Common difference is the fixed difference between the consecutive numbers of the sequence. We have to add the common difference to the preceding term, to get the next term. It can be negative or positive number. It can also have value zero.
    The formula for nth term of a arithmetic progression is given as follows:
    an = a1 + (n - 1) d
    For 20th term n = 20.
    Substituting the values in above equation we get,
    a20 = 5 + (20 - 1) 2
    = 5 + 38
    = 43
    Similarly ,
    a40 = 5 + (40 - 1)2
    = 5 + 78
    = 83
    The difference between the 40th term and 20th term is
    Difference = a40 - a20
    = 83 – 43
    = 40
    So, the difference between the 40th term and 20th term is 40.

    For such questions, we should know the formula to find any number of the terms.

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