Question

The diagram shows a circle with a centre o which is

SP divided into 9 sectors. The angles of the sectors forms an
arithmetic progression with the first sector of 4°

Calculate
(a) the common difference
(b)the angle of the largest sector
​

Answer 1

see explanation

Explanation:

The first 3 terms of the arithmetic progression are

4, 13, 22, ...

(a)

with d = 13 - 4 = 22 - 9 = 9 ← common difference

(b)

The largest sector is the 9 th and the n th term is

`a_(n)` = a + (n - 1)d

where a is the first term = 4, thus

`a_(9)` = 4 + (8 × 9 ) = 4 + 72 = 76°

Answer 2

Answer: a) 9

b) 76

Explanation:

The given arithmetic sequence is: {4, 13, 22, ... }

where a₁ = 4, a₂ = 13, a₃ = 22

The difference (d) is a₂ - a₁ --> 13 - 4 = 9

The explicit rule for an arithmetic sequence is:
`a_n=a_1+d(n-1)`

Since we are looking for the 9th term, solve for a₉

a₉ = 4 + 9(9 - 1)

= 4 + 9(8)

= 4 + 72

= 76

Check: by adding 9 to each previous term

{4, 13, 22, 31, 40, 49, 58, 67, 76, ... }
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