Sequences and Series — Class 11 Mathematics
Arithmetic Progression
An AP has a constant common difference d. Its nth term is aₙ=a+(n−1)d and sum Sₙ=n/2[2a+(n−1)d].
Worked Examples
For 5,8,11,…, a=5,d=3. The 20th term is 5+19(3)=62.
Sum of the first 20 terms =20/2(5+62)=670.
Geometric Progression
A GP has constant ratio r. Its nth term is arⁿ⁻¹. For 2,6,18,…, a=2,r=3, so the fifth term is 2×3⁴=162.
Explained MCQs
- The common difference of 7,11,15,… is 4.
- The 10th term of 3,6,9,… is 30.
- A sequence with a constant ratio is a GP.
Practice
- Find the 25th term of 4,9,14,…
- Find the sum of the first 15 terms of 2,5,8,…