Question

Find the sum of the AP

Answer 1

AP = 18 , 31/2 , 113 , ...... , -99/2

a = 18 ,d = -5/2 ,an = -99/2

n = ?

an = a + (n - 1) d

-99/2 = 18 + (n - 1) -5/2

-99/2 = 18 - (5/2)n + 5/2

-104/2 = 18 - (5/2)n

-104 = 36 - 5n

-104 - 36 = -5n

-140 = -5n

n = 28

... there are 28 terms in the given AP.

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

Sn = 28/2 [2(18) + (28 - 1) (-5/2)]

Sn = 14 [36 + (27) (-5/2)]

Sn = 14 [36 - 135/2]

Sn = 14 (-53/2)

Sn = 7(-53)

Sn = -371