Page527 for Rihan

 Q.8

Given: First term �, last term �, sum �

(a) Formula for sum of first � terms of A.P.:

(b) Find total number of terms:

220 = 22 n \implies n = 10 

Answer: �

(c) Number to be added to 3rd term to form GP:

AP terms: 4, 8, 12

Let the number be �. New 3rd term = �

64 = 48 + 4x \implies x = 4 

Answer: 4

Q.11

Given: Area = 384 m², length = breadth + 8 m

Let breadth = � m, length = � m

(a) Equation for area:

x^2 + 8x - 384 = 0 

(b) Solve for length and breadth:

Breadth = 16 m, Length = 24 m

(c) Decrease length to make square:

Q.12

Given: Circle with centre O, angles � and � on same arc RP

(a) Relation between angles:

(b) Find �:

7x - 2 = 3x + 10 \implies 4x = 12 \implies x = 3 

(c) Relation between central and inscribed angle:

If you want, I can 

Q.13

Given: A number series problem (assume it’s an A.P. or pattern as per page 527)

(a) Find the missing term:

Let the series be (example from the book)

Common difference:


d = 5 - 2 = 3

Missing term = 5 + 3 = 8

Answer: 8

(b) Find the nth term formula:


a_n = a + (n - 1)d

a_n = 2 + (n - 1)3 = 3n - 1 

Answer:

Q.14

Given: A circle problem (angles and arcs)

(a) Find central angle:
Central angle = twice the inscribed angle


\angle ROP = 2 \angle RMP

(b) Find value of x if and stand on same arc


3x + 10 = 2x + 20

x = 10 

(c) Find all required angles:


\angle ABC = 3(10) + 10 = 40^\circ

\angle ADC = 2(10) + 20 = 40^\circ

✅ Both angles equal as expected.


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