Question

The first and last term of an A P are x and y what isthe sumof A P if there are 100terms in it

Answer 1

Answer:

Step-by-step explanation:

n = 100

a= x

l= y

s100= 100/2 × x+y

50 (x+y) = Sn

Answer 2

Answer:

Sum of AP = 50x + 50y

Step-by-step explanation:

Given: First term = x and Last term = y

           Total 100 terms

To find: Sum of 100 terms

Given First term of AP i.ie., a = x

Last term of AP,i.e., l = y. Also there is only 100 terms in AP which means

100th term, l = y.

Formula of Sum of n terms when Last term is given,

$S_n=\frac{n}{2}(a+l)$

⇒  $S_{100}=\frac{100}{2}(x+y)$

⇒  $S_{100}=50\times(x+y)$

⇒  $S_{100}=50x+50y$

Therefore, Sum of AP = 50x + 50y