case based question

Question

Kanika was given her pocket money on Jan 1st, 2008. She puts ₹ 1 on Day 1, ₹ 2 on Day 2, ₹ 3 on Day 3, and continued doing so till the end of the month, from this money into her piggy bank. She also spent ₹ 204 of her pocket money and found that the end of the month she still had ₹ 100 with her. i) What is the first term and common difference? ii) What is the sum of money spent and money left with Kanika ? iii) How much was her pocket money for the month?

Answer 1

It's an arithmetic sequence with common difference = d=1

first term = a1=1

sn= sum of n terms= an(an+1)/2

1+2+3 = 3(3+1)/2 = 3(4)/2= 12/2 = 6

for a 30 day month, an=30,

an +1 = 30+1+31

sn= 1+2+3 +4 +... +28+29+30 = (30)(31)/2 = 15(31) = 465

spend 204 and have 100 left means she originally had 204+100=304