Math help for a question on sequences and series, general applications

[Mandynguyennmm]

Hi
Could i please have help for this question:
The two longest lines are each 2m long, then the next two lines are 7/4 m long and each subsequent pair of lines are 7/8 of the length of the previous lines. Find the total distance of the lines.
(diagram-zig zag pattern)

thanks

this is my working out for the question (but i am not sure why i would need to x2 or if it is the right method?because the answer is 32m)
Sinfinity= a/1-r
Sinfinity= 2/1-0.875
Sinfinity=16
=16 x 2
=total distance= 32 m

[RuiAce]

Hi
Could i please have help for this question:
The two longest lines are each 2m long, then the next two lines are 7/4 m long and each subsequent pair of lines are 7/8 of the length of the previous lines. Find the total distance of the lines.
(diagram-zig zag pattern)

thanks

this is my working out for the question (but i am not sure why i would need to x2 or if it is the right method?because the answer is 32m)
Sinfinity= a/1-r
Sinfinity= 2/1-0.875
Sinfinity=16
=16 x 2
=total distance= 32 m

The simple reason as to why you need to multiply 2 on the end is because a zig-zag actually has two lines per zig-zag to begin with.

On one hand, you got some lines that go in this direction: \
They form a GP with first term 2 and common ratio 7/8 by themselves.

On the other hand, you got lines that go in this direction: /
They form another separate GP, also with first term 2 and common ratio 7/8.

This is why you actually have two of the same geometric progression occurring. Hence the answer is \( 2\times \frac{2}{1-0.875} = 32 \)

[Mandynguyennmm]

thank you