1. ## series and sequences

A piece of wire (ABCDEF…) is used to make a pattern formed from many concentric semi-circular arcs, AB, CD, EF… joined by short intervals BC, DE, FG… The diameter of the smallest semi-circles is 8cm and each interval is 3cm.
i) What is the length of the 20th semi-circular arc?
ii) How much wire is needed to form a pattern containing 20 semi-circular arcs?

(The diagram looks like a rainbow)

This question has really confused me and i would greatly appreciate some help, the answers are 61pi (cm) and 650pi + 57

thank you to anyone who can help

2. Originally Posted by christina
A piece of wire (ABCDEF…) is used to make a pattern formed from many concentric semi-circular arcs, AB, CD, EF… joined by short intervals BC, DE, FG… The diameter of the smallest semi-circles is 8cm and each interval is 3cm.
i) What is the length of the 20th semi-circular arc?
ii) How much wire is needed to form a pattern containing 20 semi-circular arcs?

(The diagram looks like a rainbow)

This question has really confused me and i would greatly appreciate some help, the answers are 61pi (cm) and 650pi + 57

thank you to anyone who can help
Just take it in steps: what is the radius of the first arc? (4), of the second arc? (4+3), of the third arc? (4+3+3), thus the radius of the twentieth arc is...

For the second question, the length of short intervals should be simple (they have same length, and there are xxx of them); and for the length of the arcs, you have to sum the lengths of the 20 first arcs (this is the sum of a geometric progression, you may know a formula for that).