6 + 12 + 18 + 24 + … + 612 = ?
Answer और ExplanationAnswer and explanation
Answer: (A) 31518
6 + 12 + 18 + … + 612 एक AP है: a = 6, d = 6, l = 612।
n = 612 − 66 + 1 = 101 + 1 = 102
S = 1022 × (6 + 612) = 51 × 618 = 31518
✓
योग 31518 है।
6 + 12 + 18 + … + 612 is an AP with a = 6, d = 6, l = 612.
n = 612 − 66 + 1 = 101 + 1 = 102
S = 1022 × (6 + 612) = 51 × 618 = 31518
✓
The sum is 31518.
SMART APPROACH
6 × (1 + … + 102) = 6 × 102 × 1032 = 3 × 102 × 103 = 306 × 103 = 31518। जल्दी से जाँचें: 51 × 618 = 50 × 618 + 618 = 30900 + 618 = 31518। सिर्फ़ इकाई अंक (Unit digit) 8 से ही 32550 और 30558 बाहर हो जाते हैं।
6 × (1 + … + 102) = 6 × 102 × 1032 = 3 × 102 × 103 = 306 × 103 = 31518. Quick check: 51 × 618 = 50 × 618 + 618 = 30900 + 618 = 31518. The unit digit 8 alone already rules out 32550 and 30558.
Source: MTS · 11 Feb 2025 · Shift 2। Solution: Prashant Sir, Vijayastra।Source: MTS · 11 Feb 2025 · Shift 2. Solution by Prashant Sir, from Vijayastra.