CBSE NCERT Solutions Chapter 5 Arithmetic Progressions Exercise 5.3 Question 2
2. Find the sums given below:
(i)
(ii)
(iii) -5 + (-8) + (-11) + …. + (-230)
Solution (i)
First term = a = 7
Common difference = d =
Last term =
We do not know how many terms are there in the given AP. So, we need to find n first.
Using formula
, to find nth term of arithmetic progression, we can say that
Therefore, there are 23 terms in the given AP. It means n = 23.
Applying formula,
to find sum of n terms of AP, we get
Solution (ii)
First term = a = 34
Common difference = d = 32 – 34 = -2
Last term =
We do not know how many terms are there in the given AP. So, we need to find n first.
Using formula
, to find nth term of arithmetic progression, we can say that
Therefore, there are 13 terms in the given AP. It means n = 13.
Applying formula,
to find sum of n terms of AP, we get
Solution (iii)
First term = a = -5
Common difference = d = -8 – (-5) = -8 + 5 = -3
Last term =
We do not know how many terms are there in the given AP. So, we need to find n first.
Using formula
, to find nth term of arithmetic progression, we can say that
Therefore, there are 76 terms in the given AP. It means n = 76.
Applying formula,
to find sum of n terms of AP, we get
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