Question

find the sum of first fifteen terms in AP where a=-5.2 , d=-(-3.5)

Answer 1

1.    (i) Taxi fare for 1st km = Rs 15, Taxi fare after 2 km = 15 + 8 = Rs 23

Taxi fare after 3 km = 23 + 8 = Rs 31

Taxi fare after 4 km = 31 + 8 = Rs 39

Therefore, the sequence is 15, 23, 31, 39…

It is an arithmetic progression because difference between any two consecutive terms is equal which is 8. (23 – 15 = 8, 31 – 23 = 8, 39 – 31 = 8, …)

(ii) Let amount of air initially present in a cylinder.

Answer 2

Given that     a= -5.2, d= -3.5, n=15

We know that   Sn= n/2 ( 2a + (n-1)d )

S15= 15/2 ( 2* (-5.2) + (14) ( -3.5) )
       = 15/2 ( -10.4 - 49)
       = 15/2 * - 59.4
       =  -891 /2
       = -445.5