Mathematics
Grade10
Easy

Question

Determine the first term and common difference whose 3rd term is 5 and the 7th term is 9

  1. 3 , 1
  2. 4 , 2 
  3. 5 , 3
  4. 1 , 3

Hint:

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 third term and seventh term of a sequence. We are asked to find the first term and common difference.

The correct answer is: 3 , 1


    The first term of the progression is denoted by "a"
    The common difference is "d".
    The third term is a3 = 5
    The fifth term is a7 = 9
    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:
    a= a + (n – 1)d
    Let’s see the formula for fifth and seventh term.
    a3= a + (3 – 1)d
    5 = a + 2d               …(1)
    a7 = a + (7 – 1)d
    9 = a + 6d               …(2)
    Solving the equations (1) and (2). We will subtract (1) from (2).
    negative stack attributes charalign center stackalign right end attributes row a plus 6 d equals 9 end row row a plus 2 d equals 5 end row horizontal line row 4 d equals 4 end row end stack
    4d = 4
    So, d = 1
    We will substitute the value of d in equation (1).
    5 = a + 2(1)
     5 = a + 2
    a = 3
    So, the first term of the sequence is 3 and the common difference is 1.
    The right option is 1,3.

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

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