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There are n arithmetiv means between 11 and 53 such that each of them is an integer. How many distinct arithmetic progressions are possible from the above data ?

There are n arithmetiv means between 11 and 53 such that each of them is an integer. How many distinct arithmetic progressions are possible from the above data ?

Grade:10

6 Answers

Aditya Gupta
2081 Points
5 years ago
there must be 7 such aps corresponding to common difference d= 1, 2, 3, 6, 7, 14, 21, which all happen to be factors of 42, as 42= 53 – 11= (n+1)*d
SAMBHAV MISHRA
38 Points
5 years ago
Answer is 14 bro. .. Try again !
Explain again ? as soon as possible
Aditya Gupta
2081 Points
5 years ago
my answer is correct. ab tumme hi buddhi kam h to bhai main kya karu. 
11, a1, a2, …, an, 53
let common diff be d.
then 11+d= a1
an+d= 53
and an= a1+ (n – 1)d
or an + d= a1+ nd
or 53 = a1+ nd
or 53= 11+d+ nd
42= d(n+1)
d= 42/(n+1)
ab maharaj d ek integer h or 42 ko divide karta h, to d sirf 1, 2, 3, 6, 7, 14, 21, 42 hi ho sakta h kuki iske alawa 42 k koi factors hi nahi h. but obviously d cant be 42 as n cant be zero. hence there will be ONLY 7 POSSIBLE VALUES.
kuch bhi comment karne or disapprove karne se pehle thodi buddhi ka bhi prayog kar liya karo agar ho tumhare pas. or agar ab bhi tumhe mera answer gakat lagta ho to reason k sath prove krdo or main yahan p tutoring karna chhor dunga.
SAMBHAV MISHRA
38 Points
4 years ago
first of all mind your language.... and second answer is 14 only.. here is the explanation
n arithmetic means are in between a and b; d = b-a/n+1
evaluate for how many values of (n+1), d is an integer. 
@aditya gupta tumhari budhi ghass khane gayi hai !
Kush
13 Points
3 years ago
Answer will be 14because 42 is divisible by only1,2,3,6,7,14,21. But now in the question it is mentioned integers so  42 will be divisible by -1,-2,-3,-6,-7,-14,-21. So there are a total of 14 factors
Idontknow
13 Points
3 years ago
Hey guys answer will be 7 only and not 14... d = b-a/n+1 it’s gn that d is integer but d must be positive since , the last term of the AP(53) is greater than first term(11). 42 is divisible by -1 , -2 ,-3...so on but to obtain these , n+1 = -1 ,-2 ,-3 .. so on  → which implies n is negative or zero ...n is no.of arithmetic means...how it could be negative? It can’t be zero since n belongs to N..So the answer must be 7..Pls check urs guys..

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