Class 10 Maths — Chapter 5: ARITHMETIC PROGRESSIONS

What you'll learn

• ▸Defining an Arithmetic Progression (AP)
• ▸First Term (a) and Common Difference (d)
• ▸General Form of an AP
• ▸Verifying if a Sequence is an AP
• ▸Generating Terms of an AP
• ▸Finite vs. Infinite APs
• ▸Modeling Real-World Situations with APs

Chapter Summary

--- PAGE 1 --- 1062CH05 ARITHMETIC PROGRESSIONS 5 5.1 Introduction You must have observed that in nature, many things follow a certain pattern, such as the petals of a sunflower, the holes of a honeycomb, the grains on a maize cob, the spirals on a pineapple and on a pine cone, etc. We now look for some patterns which occur in our day-to-day life. Some such examples are : (i) Reena applied for a job and got selected. She has been offered a job with a starting monthly salary of ₹ 8000, with an annual increment of ₹ 500 in her salary. Her salary (in ₹) for the 1st, 2nd, 3rd, ... years will be, respectively 8000, 8500, 9000,.... (ii) The lengths of the rungs of a ladder decrease uniformly by 2 cm from bottom to top (see Fig. 5.1). The bottom rung is 45 cm in length. The lengths (in cm) of the 1st, 2nd, 3rd, ..., 8th rung from the bottom to the top are, respectively 45, 43, 41, 39, 37, 35, 33, 31 Fig. 5.1 5 (iii) In a savings scheme, the amount becomes — ti…

Practice Questions from this Chapter

Tap "Get Solution" on any question to ask our AI tutor.

1. Identify APs quickly? Get Solution →
2. Calculate common difference easily? Get Solution →
3. Apply APs in real-world problems? Get Solution →
4. What defines a list of numbers as an Arithmetic Progression (AP)? Get Solution →
5. In an AP, what is the 'common difference'? Get Solution →
6. What is the general form of an AP, where 'a' is the first term and 'd' is the common difference? Get Solution →
7. An AP that has a limited number of terms and a last term is called a... Get Solution →
8. What is the minimum information needed to define a specific Arithmetic Progression? Get Solution →

Did you know?

• 💡 Sunflower seeds grow in spirals related to a famous number sequence called Fibonacci.
• 💡 Ancient Egyptians used number patterns to build pyramids and design their temples.
• 💡 The oldest known math textbook, over 3600 years old, contains problems with arithmetic progressions.
• 💡 Bees build hexagonal honeycomb cells because hexagons fit perfectly together with no gaps.
• 💡 Our brains are wired to constantly look for patterns, even when none truly exist.

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