Arithmetic
Progressions
To find d
Q.5. The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms of A.P and the common difference.
Sol:
For an A.P a = 5,
∴
400
=
∴
400
=
∴
400
=
∴
=
∴
∴
∴
∴
∴
∴
∴
25
1
8
3
an = 45,
Sn = 400
For the given value of Sn let’s use the formula
To find n
For given value of an. Let’s use the formula
For Sn substitute,
a = 5, an = 45 & Sn = 400
For an substitute,
a = 5, an = 45 & n = 16
Exercise 5.3 5
6) The first and last terms of an AP are 17 and 350 respectively. If the
common difference is 9, how many terms are there and what is their sum?
Sol:
For given AP:
a = 17,
an = 350,
d = 9
For given value of an,
Lets use the formula
We know that,
an =
a + (n – 1)d
Substitute,
a = 17, d = 9 & an = 350
∴ 350 =
17
+ (n – 1)
(9)
∴ 350 – 17 =
(n – 1)(9)
∴ 333 =
(n – 1)(9)
= n – 1
∴ 37 =
n – 1
∴ n = 38
We need to find no. of terms i.e. value of ‘n’
We need to find their sum i.e. value of ‘Sn’
Sn =
For Sn substitute,
n = 38, a = 17 & an = 350
∴ S38 =
=
19
(367)
∴ S38 =
6973
∴ There are 38 terms & their sum is 6973.
Exercise 5.3 6