Arithmetic Progressions Exercise 5.4
NCERT solutions for Maths Arithmetic Progression
NCERT Solutions for Class 10 Maths Arithmetic Progressions
1. Which term of the AP: 121, 117, 113, ….. is its first negative term?
Ans. Given: 121, 117, 113, …….
Here 
Now, 
= 
= 
= 
For the first negative term, 
is an integer and 
Hence, the first negative term is 32nd term.
NCERT Solutions for Class 10 Maths Exercise 5.4
2. The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of sixteen terms of the AP.
Ans. Let the AP be 
Then, 
……….(i)
Also 
Taking 
= 
= 
= 
= 76
Taking 
,
= 
= 
= 
= 20
and 76
NCERT Solutions for Class 10 Maths Exercise 5.4
3. A ladder has rungs 25 cm apart (see figure). The rungs decrease uniformly in length from 45 cm, at the bottom to 25 cm at the top. If the top and the bottom rungs are 
m apart, what is the length of the wood required for the rungs?
Ans. Number of rungs 
= 10
The length of the wood required for rungs = sum of 10 rungs
= 
= 
= 350 cm
NCERT Solutions for Class 10 Maths Exercise 5.4
4. The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of 
such that the sum of the numbers of the houses preceding the house numbered is equal to the sum of the numbers of the houses following it. Find this value of 
Ans. Here 
and 
= 
= 
= 
= 
= 
= 
= 49 x 25
According to question,
= 
+ = 
=
Since, is a counting number, so negative value will be neglected.
NCERT Solutions for Class 10 Maths Exercise 5.4
5. A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete.
Each step has a rise of 
m and a tread of 
m (see figure). Calculate the total volume of concrete required to build the terrace.
Ans. Volume of concrete required to build the first step, second step, third step, ……. (in m2) are
Total volume of concrete required = 
= 
= 
= 
= 