Question

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?

Answer 1

Amount spent on 1^st day = Rs. 10

Amount spent on 2^st day = Rs. 20

Amount spent on 3^rd 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 × 4095

= 40950

Hence, the total amount spent in 12 days is Rs. 40950.