Mathematics
Grade10
Easy

Question

Find the 11th term of the Arithmetic Sequences : -3 , fraction numerator negative 1 over denominator 2 end fraction , 2………

  1. 10
  2. 25
  3. 22
  4. 23

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 sequence. We are asked to find the 11th term. We will find the common difference first.

The correct answer is: 22


    The given sequence is -3,  negative 1 half, 2, ... 
    The first term of the progression is a = -3
    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 common difference is
    d space equals space minus fraction numerator space 1 space over denominator 2 end fraction minus left parenthesis negative 3 right parenthesis
space space space equals space minus 1 half space plus space 3
space space space equals space fraction numerator negative 1 space plus space 6 over denominator 2 end fraction
space space space equals space 5 over 2
space space
space space space space space
    The formula for nth term of a arithmetic progression is given as follows:
    an = a + (n – 1)d
    We will substitute n = 11 to find the 11th term.
    a11 = -3 + (11 - 1) 5 over 2
    = -3 + 25
    = -22
    So, the 11th term is 22.

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

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