What is the sum of the series

Question

-64,-66,-68,.........,-100

Answer 1

Given AP  -64,-66,-68,.........,-100

t1  =  a  =  -64

t2  =  -66

d  =  t2 - t1

    =  -66  -  (-64)

    =  -66 + 64

d  =  -2

nth term tn = a + (n-1)d --------------> (1)

Substitute a  =  -64 and d  =  -2 and tn = -100 in Eq (1)

-100  =  -64 + (n-1)(-2)

-100  =  -64 -2n +2

-100  =  -62 - 2n

2n  =  -62 + 100

2n = 38

n  =  38/2

n  =  19

Sum of the numbers in AP 

Sn  =  n/2 (a + l) --------> (2)

Substitute n =19, First term (a) = -64 and Last Term (l) = -100 in Eq (2)

S19  =  19/2 (-64 -100)

        =   19/2 (-164)

        =  19 X (-82)

s19  =  -1558

Amswer :

The sum of the series is -1558.