CBSE NCERT Solutions Chapter 5 Arithmetic Progressions Exercise 5.3 Question 3
3. In an AP
(i) given
, find n and
.
(ii) given
, find d and
.
(iii) given
, find a and
.
(iv) given
,
, find d and
.
(v) given
, find a and
.
(vi) given
, find n and
.
(vii) given
, find n and d.
(viii) given
, find n and a.
(ix) given
, find d.
(x) given
, and there are total of 9 terms. Find a.
Solution (i)
Given
, find n and
.
Using formula
, to find nth term of arithmetic progression, we can say that
Applying formula,
to find sum of n terms of AP, we get
Therefore,
and
Solution (ii)
Given
, find d and
.
Using formula
, to find nth term of arithmetic progression, we can say that
Applying formula,
to find sum of n terms of AP, we get
Therefore,
and
Solution (iii)
Given
, find a and
.
Using formula
, to find nth term of arithmetic progression, we can say that
Applying formula,
to find sum of n terms of AP, we get
Therefore,
and
Solution (iv)
Given
,
, find d and
.
Using formula
, to find nth term of arithmetic progression, we can say that
(1)
Applying formula,
to find sum of n terms of AP, we get
Putting (1) in the above equation, we get
Using formula
, to find nth term of arithmetic progression, we can say that
Putting value of
and equation (1) in the above equation, we get
Therefore,
and
Solution (v)
Given
, find a and
.
Applying formula,
to find sum of n terms of AP, we get
Using formula
, to find nth term of arithmetic progression, we can say that
Therefore,
and
Solution (vi)
Given
, find n and
.
Applying formula,
to find sum of n terms of AP, we get
We discard negative value of n because here n cannot be in negative or fraction. The value of n must be a positive integer.
Therefore,
Using formula
, to find nth term of arithmetic progression, we can say that
Therefore,
and
Solution (vii)
Given
, find n and d.
Using formula
, to find nth term of arithmetic progression, we can say that
(1)
Applying formula,
to find sum of n terms of AP, we get
Putting equation (1) in the above equation, we get
Putting value of
in equation (1), we get
Therefore,
and
Solution (viii)
Given
, find n and a.
Using formula
, to find nth term of arithmetic progression, we can say that
(1)
Applying formula,
to find sum of n terms of AP, we get
Putting equation (1) in the above equation, we get
Here, we cannot have negative value of
. Therefore, we discard negative value of
which means
.
Putting value of
in equation number (1), we get
Therefore,
and
Solution (ix)
Given
, find d.
Applying formula,
to find sum of n terms of AP, we get
Solution (x)
Given
, and there are total of 9 terms. Find a.
Applying formula,
, to find sum of n terms, we get
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