Question

on 1st jan,sanika decide to save rs 10,rs 11 on second day,rs 12 on third day. if she decides to save like this,then on 31st dec 2016 what would be her total saving?

Answer 1

On 1st Jan,
She saved 10 Rs.
    Next Day 11 Rs.
    Next Day 12 rs

So money saved by her
= 10 + 11 + 12 + 13 + .........................+ (till 31st Dec)

Now, Above Sum is the sum of a Arithmetic Progression with
a = 10
d = 1
n = 366 ( since year 2016 is a Leap Year)

=>Sum of an A.P. = (n/2){ 2a + (n-1)d}
                                  = (366/2){ 20 + 365 }
                                  = 70455

So, she saved Rs. 70455 till the end of the year

Answer 2

on 1st jan she saved 10 rs next day she saved 11 rs next day she saved 12 rs
so money saved by her = 10 +12+13.......+(till 31st dec).
by arithmetic progression a=10 d= 1 n=366 (as 2016 is a leap year).
sum of an AP = ( n/2(2a+(n_1)d)
=366 (20 +365)
=70455