An employee receives two components of income each year: • Basic pay: ₹3,60,000 in…
MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
An employee receives two components of income each year:
• Basic pay: ₹3,60,000 in the first year, increasing by ₹21,000 every following year.
• Annual bonus: ₹24,000 in the first year, increasing by ₹3,000 every following year.
Using this information, answer the questions below:
(i) Show that the total cash received at the end of each year forms the term‐wise sum of two arithmetic progressions and hence express the cash received in the nth year as a single expression in n.
(ii) Compute the cumulative cash received during the first 10 years of service.
(iii) Determine the least number of complete years after which the employee’s cumulative cash received will exceed ₹1,00,00,000. Show all working clearly.