Question

. Daya gets pocket money from his father every day.
Out of the pocket money, he saves
2.75 on first day, 3.00 on second day,
cond day, 3.25 on third day and so on. Find :
3.25 on third day and so
(i) the amount saved by Daya on 14th day
(ii) the amount saved by Daya on 30th day.
iii) the total amount saved by him in 30 days.

Answer 1

1. 6 rupees -use an=a+(n-1)d
2. 11.25 rupees an=a+(n-1)d
3. 191.25. use. Sn=n/2[2a+(n-1)d]

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Answer 2

i) The amount saved by Daya on 14th day = Rs 6

ii)The amount saved by Daya on 30th day = Rs 10

iii)The total amount saved by him in 30 days = Rs 191.25

Explanation:

We can see that , the amount of saving 2.75 , 3.00 , 3.25  , ........ is following Arithmetic progression as difference between each two consecutive day's savings is common as d=0.25.

Formula : nth term of A.P.

$a_n=a+(n-1)d$

Put a= 2.75 and d= 0.25, we get

Amount saved by Daya on nth day = $2.75+(n-1)0.25 = 2.75+0.25n-0.25=0.25n+2.5$

i.e.  Amount saved by Daya on nth day = $0.25n+2.5$

i) n=14

$a_{14}=0.25(14)+2.5=6$

The amount saved by Daya on 14th day = rs 6

ii) n= 30

$a_{30}=0.25(30)+2.5=10$

The amount saved by Daya on 30th day = rs 10

iii)Formula : sum of first n terms = $S_n=\dfrac{n}{2}(a+a_n)$

$S_{30}=\dfrac{30}{2}(2.75+10)=191.25$

The  total amount saved by him in 30 days = Rs 191.25

# Learn more :

From your pocket money you save 1 on one day 2 on second.Day 3 on third day and so on. How much money will you save in the month of march 2008

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