# A Boy Spends Rs.10 on First Day, Rs.20 on Second Day, Rs.40 on Third Day and So On. Find How Much, in All, Will He Spend in 12 Days? - Mathematics

Sum

A boy spends Rs.10 on first day, Rs.20 on second day, Rs.40 on third day and so on. Find how much, in all, will he spend in 12 days?

#### Solution

Amount spent on 1st day = Rs. 10
Amount spent on 2st day = Rs. 20
Amount spent on 3st day = Rs. 40 and so on

Now, 20/10=2, 40/20=2,

Thus, 10, 20, 40, ...... is a G.P. with first term, a = 10 and common ratio, r = 2 (r > 1)

∴ Total amount spent in 12 days = S12

"S"_n=(a(r^n-1))/(r-1)

=>"S"_12=(10(2^12-1))/(2-1)= 10(212-1) = 10(4096 - 1) = 10 x 4095 = 40950
Hence, the total amount spent in 12 days is Rs. 40950.

Concept: Geometric Progression - Finding Sum of Their First ‘N’ Terms
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#### APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 11 Geometric Progression
Exercise 11 (D) | Q 4 | Page 161