Question

check weather 301 is a term of the ap 5,10,17



what is the perimeter of a sector of a circle whose central angle is 60 degree and radius 7 cm.


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Answer 1

Answer

1)It is not an A.P

2)7.33cm

Step-by-step explanation:

1)

A.P:5,10,17....

5,10,17 is not a A.P as the common differences not equal between 10 and 5; and 17 and 10.

2)Perimeter of sector= θ/360×2πr

=60/360×2×22/7×7

=1/6×44

=1×7.33

=7.33cm

Answer 2

AnswEr :

Question 1

Check whether 301 is a term of the AP : 5,10,15......

Given sequence,

5,10,15,.................

Let a and d be the first term and common difference of the above AP (a,d) = (5,5)

To check whether 301 is a term of the above sequence

Let the nth term be 301

Thus,

$\sf \: 301 = 5 + (N - 1)5 \\ \\ \longrightarrow \: \sf \: 301 = 5N + \cancel{5 - 5} \\ \\ \longrightarrow \: \sf \: N = \dfrac{301}{5}$

For any value of N,'N' can't be a rational. Only if N is a natural number,the given term would be a part of the above sequence

Thus,301 isn't a term in the given AP

$\rule{300}{2}$

Question 2

From the Question,

• Radius of the Circle : 7 cm

• Central Angle : 60°

We have to find the perimeter of the sector formed by the arc

$\boxed{\boxed{\sf Perimeter \ of \ Sector = \dfrac{\theta}{360}\times 2 \pi r}}$

(Substituting the values)

$\longrightarrow \sf Perimeter = \dfrac{60}{360}\times 2 \times \dfrac{22}{\cancel{7}} \times \cancel{7} \\ \\ \longrightarrow \sf Perimeter = \dfrac{22}{3} cm \\ \\ \large{\longrightarrow \boxed{\boxed{\sf Perimeter = 7.33 \ cm }}}$

$\rule{300}{2}$

$\rule{300}{2}$