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Arithmetic Progressions

Question
CBSEENMA10007904
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A 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 Fig. 5.4. What is the total length of such a spiral made up of thirteen consecutive semicircles?  open parentheses Take space straight pi space equals space 22 over 7 close parentheses



Solution

We know that,
Length of semicircle = πr
l1, = π x 0.5 cm
l2 = π x 1.0 cm
3 = π x 1.5 cm
And, l4 = π x 2.0 cm and so on.
Let l be the total length of such a spiral made up of thirteen consecutive semi-circles.

Hence, total length of such a spiral made up of thirteen consecutive semi-circles = 143 cm. Ans.

Some More Questions From Arithmetic Progressions Chapter

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?

The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a – 10, d = 10

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a = –2, d = 0

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a = 4, d = – 3

Write first four terms of the AP, when the first term a and the common difference d are given as follows:

a = – 1.25, d = – 0.25

For the following APs, write the first term and the common difference
3, 1, – 1, – 3, . . .

For the following APs, write the first term and the common difference
– 5, – 1, 3, 7, . . .

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