6.11 Real Life Problems involving Sequences and Series

6.11 Real Life Problems involving Sequences and Series

Example 27 — Vehicle arrivals

Cars arrive $4$ every $5$ minutes: A.P. $4, 8, 12, \ldots$ with $d = 4$. After $1$ hour ($n = 12$): $a_{12} = 48$ cars.

Example 28 — Simple interest

Rs. $50000$ at $8\%$ simple interest for $11$ years: interest A.P. $4000, 8000, \ldots$ so $a_{11} =$ Rs. $44000$.

Example 29 — Compound interest

Rs. $200000$ at $5\%$ compounded annually for $10$ years: amount $P(1.05)^{10} \approx$ Rs. $325778.92$.

Example 30 — Grid columns

$12$ columns, first width $50$px, each $+10$px: $S_{12} = 1260$px.

Example 31 — Motor vehicle leasing

$a_1 = 15000$, $d = 500$, $n = 24$:

1. $a_{24} =$ Rs. $26500$
2. $S_{24} =$ Rs. $498000$
3. Budget Rs. $400000$ is insufficient for $24$ months.
4. Maximum $n$ with $S_n \le 400000$ is $n = 20$.