Question
Sun November 13, 2011 By: Gurleen Kaur
 

1.If the sum of the AP 3, 7, 11,............ is 210,the number of term is ________ a)10 b)12 c)15 d)22 2. If the sum to 1st 'n' terms of an AP is 3n square+2n, find the AP

Expert Reply
Sun November 13, 2011
Ans 1-
 
given AP 3,7,11,15,19.....
 
Sum of terms = 210
 
Let us say number of terms is n.
 
Hence sum= n(2a+(n-1)d)/2
 
Now, first term = a = 3
 
d= common difference = 7-3 = 4
 
putting these values we get
 
210=n(6+4(n-1))/2
 
210 = n(3+2n-2)
 
210= n(2n +1)
 
2n2 + n -210 = 0
 
2n2 + 21n-20n-210 = 0
 
n(2n+21)-10(2n-21) = 0
 
(n-10)(2n+21)=0
 
So, n = 10 or n =-21/2, it can not be n because n is number of terms that can not be negative.
 
So correct value is n=10
 
2) Sum of first n terms of AP, Sn = 3n2 + 2n
 
Now choose n =1 and put in the above formula since
 
this means sum of first 1 term that is the first term only = 3+2 = 5
 
Now put n=2 to get the sum of first two terms = 3×4 + 2×2 = 12+4 = 16
 
This means 
 
first term + second term = 16
 
but first term =5 as calculated above
 
so, second term = 16-5 = 11
 
So common difference becomes, 11-5 = 6
 
So the AP becomes, 5, 11, 17, 23......
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