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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

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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