Q10 of 202 Page 10

The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by , then k=

Let the common difference and number of terms of AP be d and n respectively.


Last term of AP = an = l (given)


l = a + (n–1) d


n = + 1……………… (1)


S= (2a + (n–1) d)


S = + 1) (2a + ( + 1 –1) d) …………… using (1)


S= + 1) (2a + l –a)


S= + 1) (a + l)


( + 1) =


= –1


=


D =


Comparing this with


We get k =2S

More from this chapter

All 202 →
8

If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are

 9

Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn – kSn–1 + Sn–2, then k =

 11

If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =

 12

If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is