Arithmetic Progressions
AP problems in daily life
Solve everyday problems with the nth term of an AP.
Many real situations grow or shrink by the same amount each step, and that makes them APs. The skill is to spot a (where it starts) and d (the fixed change). Then aₙ = a + (n – 1)d does the rest.
Say in words what each term means. In a garden, a₁ is 'plants in the first row' and a₁₀ is 'plants in the 10th row'.
| Situation | a | d | Question → answer |
|---|---|---|---|
| Simple interest on ₹1000 at 8% (total after each year) | 80 | 80 | after 30 years: 80 + 29 × 80 = ₹2400 |
| Rose plants: 23, 21, 19 … 5 in a row | 23 | –2 | how many rows? 5 = 23 + (n – 1)(–2) → 10 rows |
| Subba Rao's salary: 5000, 5200 … | 5000 | 200 | when ₹7000? → 11th year |
| Ramkali's weekly savings: 5, 6.75, 8.50 … | 5 | 1.75 | when ₹20.75? → week 10 |
Simple interest makes an AP because the same interest is added every year. Compound interest does not: it grows by more each year.
When do two APs give the same number? Write both nth terms and set them equal. For 63, 65, 67, … and 3, 10, 17, …: 63 + 2(n – 1) = 3 + 7(n – 1), so 60 = 5(n – 1) and n = 13.
Check your answer makes sense. Rows, weeks and years are whole numbers, and they can't be negative.
Practise this lesson
Questions that get harder as you improve, a Tutor that helps without giving the answer away, and progress you can see. Free for every learner.
No account, no email address. Opens the real product.