Q26 of 49 Page 1

If the sum of first 4 terms of an A.P. is 40 and that of first 14 terms is 280, find the sum of its first n terms.

Or


Find the sum of the first 30 positive integers divisible by 6.

Sum of n terms of an A.P., Sn =

Where a=First term, d=Common difference, n=No. in terms


For n=4, S4= (given)


⇒ 2a + 3d=20


⇒ 2a=20-3d ………….(1)


For n=14,S14= (given)


⇒ 2a + 13d=40 ………..(2)


Putting the value of 2a in eq(2) from eq(1)


⇒ 20-3d + 13d=40


⇒ 20 + 10d=40


⇒ 10d=20


⇒ d=2


Putting value of d in eq(1), we get


⇒ 2a=20-3(2)=20-6=14


⇒ a=7


Sum of n terms, Sn =


Sn =


Sn =n[7 + n-1]


Sn =n(n + 6)=n2 + 6n


Or


The first 30 positive integers divisible by 6 are 6,12,18,24…..


We see that these are in A.P.


With a=6 and d=12-6=6


Sum of n terms, Sn =


S30=


S30=15(186)=2790


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