NCERT Mathematics · Class 10 · English · 2026-27
Arithmetic Progressions — Exercise 5.4
Independently written, step-by-step solutions. Prompts below are concise paraphrases; use the official textbook for the complete question wording.
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Question 1
Locate the first negative term of 121,117,113,… .
Step-by-step solution
Optional enrichment exercise in the NCERT textbook.
aₙ=121−4(n−1)=125−4n. For negativity, n>125/4=31.25. The smallest positive integer is n=32. The 31st term is 1 and the 32nd is −3.
Resource ID: CB-10-M-CH5-EX5.4-Q1
Question 2
Given a₃+a₇=6 and a₃a₇=8, find S₁₆.
Step-by-step solution
Optional enrichment exercise in the NCERT textbook.
Let u=a₃ and v=a₇. They are the roots of t²−6t+8=(t−2)(t−4)=0. If u=2,v=4, then 4d=2, d=1/2 and a=u−2d=1; S₁₆=8(2+15/2)=76. If u=4,v=2, then d=−1/2 and a=5; S₁₆=8(10−15/2)=20.
Resource ID: CB-10-M-CH5-EX5.4-Q2
Question 3
Rungs are 25 cm apart over a 2.5 m span; lengths decrease uniformly from 45 to 25 cm. Find total rung wood.
Step-by-step solution
Optional enrichment exercise in the NCERT textbook.
The 250 cm span has 250/25=10 gaps, so there are 11 rungs, including both endpoints. Their lengths form an AP. Total=11(45+25)/2=385 cm.
Resource ID: CB-10-M-CH5-EX5.4-Q3
Question 4
Find a house x among 1–49 with equal sums before and after it.
Step-by-step solution
Optional enrichment exercise in the NCERT textbook.
The total of 1,…,49 is 49×50/2=1225. Equality requires x(x−1)/2=1225−x(x+1)/2. Multiplying by 2 and simplifying gives 2x²=2450, hence x²=1225. Since the house number is positive, x=35. The sums on both sides are 595.
Resource ID: CB-10-M-CH5-EX5.4-Q4
Question 5
Find the concrete volume of a 15-step terrace, 50 m long, rise 1/4 m and tread 1/2 m.
Step-by-step solution
Optional enrichment exercise in the NCERT textbook.
Split the solid into fifteen vertical strips of width 1/2 m, length 50 m, and heights 1/4,2/4,…,15/4 m. The volumes are (50×1/2×1/4)k=6.25k m³. Total=6.25(1+2+⋯+15)=6.25×120.
Resource ID: CB-10-M-CH5-EX5.4-Q5