The sum of integers from 1 to 100 that are divisible by 2 or 5 is ____


Question and Answers Forum

All Questions Topic List
UNKNOWN Questions
Previous in All Question Next in All Question
Previous in UNKNOWN Next in UNKNOWN
Question Number 43765 by peter frank last updated on 15/Sep/18

$The sum of integers from 1 to 100 that$ $are divisible by 2 or 5 is_____.$
	Answered by math1967 last updated on 15/Sep/18
	$sum of divisible by 2=S_2 sum of divisible by 5=S_5 sum of divisible by both 2 and5=S_(10) ∴n(S_2 ∪S_5 )=n(S_2 )+n(S_5 )−n(S_2 ∩S_5 ) ={2+4+...100}+{5+10+..100} −{10+20+...100} =((50)/2)(2×2+49×2)+((20)/2)(2×5+19×5) −((10)/2)(2×10+9×10) [using S_n =(n/2){2a+(n−1)×d}] =2550+1050−550=3050Ans$
	$s u m o f d i v i s i b l e b y 2 = S_{2}$ $s u m o f d i v i s i b l e b y 5 = S_{5}$ $s u m o f d i v i s i b l e b y b o t h 2 a n d 5 = S_{10}$ $∴ n (S_{2} \cup S_{5}) = n (S_{2}) + n (S_{5}) - n (S_{2} \cap S_{5})$ $= {2 + 4 + . . . 100} + {5 + 10 + . . 100}$ $- {10 + 20 + . . . 100}$ $= \frac{50}{2} (2 \times 2 + 49 \times 2) + \frac{20}{2} (2 \times 5 + 19 \times 5)$ $- \frac{10}{2} (2 \times 10 + 9 \times 10)$ $[u s i n g S_{n} = \frac{n}{2} {2 a + (n - 1) \times d}]$ $= 2550 + 1050 - 550 = 3050 A n s$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum