Question

The first and last terms of an ap are x and y respectively what is the sum of the ap if there are hundred terms in it

Answer 1

given
total term in Ap ( n) = 100
a= x, l= y
so
Sn= n/2(a+l)
S100 = 100/2(x+y)
= 50(x+y)
or 50x+50y

Answer 2

Answer:

100[ ( x + y ) ] / 2

Step-by-step explanation:

we know that first term is x and last term is y

the formula of sum of numbers in AP is   n/2 [ 2a + (n-1) d ]

                                                              is   n/2 [ a + a + (n-1) d ]

                                                              is   n/2 [ a + nth term ]

                                                              is   n [ (a + nth term) / 2 ]  

so in this question 'a' is x and 'n' is 100 and nth term is 100th term = y

so by substituting the values we get

100 [ x+y] / 2          

= 50 [ x+y ]

hope helped