Arithmetic Progressions — Question Ex 5.3 Q18
Back to all questionsA spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm,… as shown in figure. What is the total length of such a spiral made up of thirteen consecutive semicircles?
(Take π = \(\frac { 22 }{ 7 }\))
[Hint: Length of successive semicircles is l1, l2, l3, l4, … with centres at A, B, respectively.]
CBSE Class 10 Arithmetic Progressions — Complete Guide
AP is a high-scoring chapter carrying 5-6 marks. The nth term and sum formulae appear in every board exam.
Quick Revision: Key Concepts
- AP: a, a+d, a+2d, ... (constant common difference)
- nth term: an = a + (n−1)d
- Sum: Sn = n/2[2a + (n−1)d] = n/2(a + l)
- Key relation: an = Sn − Sn−1
Most Important Questions
- Find specific terms (nth term, last term)
- Find sum of first n terms
- Find number of terms when sum is given
- Application problems (salary, savings, stacking)
About Bright Tutorials
Bright Tutorials, Hariom Nagar, Nashik Road, provides expert coaching for CBSE and ICSE students. Our experienced faculty ensures comprehensive preparation for board exams with personalised attention and 3-tier differentiation for students of all levels. Contact us at 9403781999 or visit brighttutorials.in.