NCERT MATHS CLASS - X
Arithmetic Progressions
Exercise 5.4
Question 1:
Which term of the A.P. 121, 117, 113 … is its first negative term?
[Hint: Find n for an < 0]
Given A.P. is 121, 117, 113 …
a = 121
d = 117 − 121 = −4
an = a + (n − 1) d
= 121 + (n − 1) (−4)
= 121 − 4n + 4
= 125 − 4n
We have to find the first negative term of this A.P.
Therefore, 32nd term will be the first negative term of this A.P.
Question 2:
The sum of the third and the seventh terms of an A.P is 6 and their product is 8. Find the sum of first sixteen terms of the A.P.
We know that,
an = a + (n − 1) d
a3 = a + (3 − 1) d
a3 = a + 2d
Similarly, a7 = a + 6d
Given that, a3 + a7 = 6
(a + 2d) + (a + 6d) = 6
2a + 8d = 6
a + 4d = 3
a = 3 − 4d .........(i)
Also, it is given that (a3) × (a7) = 8
(a + 2d) × (a + 6d) = 8
From equation (i),
From equation (i),
