CBSE NCERT Solutions Chapter 5 Arithmetic Progressions Exercise 5.2 Question 9
9. If the third and the ninth terms of an AP are 4 and -8 respectively, which term of this AP is zero?
Solution:
It is given that 3rd and ninth term of AP are 4 and -8 respectively.
It means
and
where,
and
are third and ninth terms respectively.
Using formula
, to find nth term of arithmetic progression, we get
4 = a + (3-1)d And, -8 = a + (9-1)d
And,
These are equations in two variables. Lets solve them using method of substitution.
Using equation
, we can say that
.
Putting value of
in other equation
, we get
Putting value of
in equation
, we get
Therefore, first term
and Common Difference
We want to know which term is equal to zero.
Using formula
, to find nth term of arithmetic progression, we get
Therefore, 5th term is equal to
.
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