Solution:

We are aware that,

The perimeter of a semi-circle is πr

Therefore,

_P1 = π(0.5) = π/2 cm

_P2 = π(1) = π cm

_P3 = π(1.5) = 3π/2 cm

We can say that, P_1, P₂, P₃ are the lengths of the semi-circles.

As a result a series is formed here, as,

π/2, π, 3π/2, 2π, ….

P₁ = π/2 cm

P₂ = π cm

The common difference, d = P₂ – P₁ = π – π/2 = π/2

First term = P₁= a = π/2 cm

Using the sum of n term formula, we know,

S_n = n/2 [2a + (n – 1)d]

As a result, the sum of the length of 13 consecutive circles is;

S₁₃ = 13/2 [2(π/2) + (13 – 1)π/2]

=  13/2 [π + 6π]

=13/2 (7π)

= 13/2 × 7 × 22/7

= 143 cm