This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Answer
1.13n$) is 15.
Here are the solutions to the problems.
The initial salary of Mr. Lutta is sh. 42,000 per annum. His salary increases by 13% each year. Determine his total earnings after 15 years. Give your answer to the nearest thousands.
Step 1: Identify the type of progression. This is a geometric progression where the initial salary is the first term (), and the annual increase of 13% means the common ratio () is . The number of years () is 15. We need to find the sum of the first 15 terms ().
Step 2:
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This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.