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Question
In the following situation, involved make an arithmetic progression? and why?
The amount of money in the account every year, when ₹ 10000 is deposited at compound interest at 8% per annum.
Solution
The amount at the end of 1st year
= `10000 (1 + 8/100)^1`
The amount at the end of 2nd year
= `10000 (1 + 8/100)^2`
The amount at the end of 3rd year
= `10000 (1 + 8/100)^3`
The amount at the end of 4th year
= `10000 (1 + 8/100)^4`
∴ The terms are
`1000 [10000 (1 + 8/100)]`
`[10000 (1 + 8/100)^2], [10000 (1 + 8/100)^3],...`
Obviously,
`[10000 (1 + 8/100)] - [10000]`
`≠ [10000 (1 + 8/100)^2] - [10000 (1 + 8/100)]`
∴ The above terms are not in A.P
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