41 + 42 + 43 + … + 70 = ?
Answer और ExplanationAnswer and explanation
Answer: (C) 1665
41, 42, …, 70 एक AP है जिसमें a = 41, l = 70, d = 1।
पदों (Terms) की संख्या n = 70 − 41 + 1 = 30
S = n2(a + l) = 302 × (41 + 70)
= 15 × 111 = 1665
✓
योग 1665 है।
41, 42, …, 70 is an AP with a = 41, l = 70, d = 1.
Number of terms n = 70 − 41 + 1 = 30
S = n2(a + l) = 302 × (41 + 70)
= 15 × 111 = 1665
✓
The sum is 1665.
SMART APPROACH
(1 + … + 70) − (1 + … + 40) = 70 × 712 − 40 × 412 = 2485 − 820 = 1665। या सीधे: 30 पद (Terms) × औसत (Average) 55.5 = 1665।
(1 + … + 70) − (1 + … + 40) = 70 × 712 − 40 × 412 = 2485 − 820 = 1665. Or simply: 30 terms × average 55.5 = 1665.
Source: MTS · 12 Feb 2025 · Shift 1। Solution: Prashant Sir, Vijayastra।Source: MTS · 12 Feb 2025 · Shift 1. Solution by Prashant Sir, from Vijayastra.