Question

Answer the following questions. 1. The first term of an A.P. is 5, the last term is 45 and the sum of all its terms is 400. Find the number of terms and the common difference. (4 Marks) 2. A circle touches all the four sides of a quadrilateral ABCD. Prove that AB+CD=AD+BC. (2 Marks) 3. Draw a line segment AB of length 9 cm. Taking A as centre, draws a circle of radius 4cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle. (4 marks)​

Answer 1

Answer:

Step-by-step explanation:

Given that, Sn=400, An= 45 and a=5

An=45

a+(n-1)d=45

(n-1)d=40

And,Sn=400

n/2{2a+(n-1)d}=400

n{2a+(n-1)d}=800

n{2×5+40}=800 {As a=5,(n-1)d=40}

n=800/50=16 =Number of terms

And,we have

(n-1)d=40

d=40/15=2.67=Common Difference

Answer 2

Step-by-step explanation:

1) t1=a=5 , tn=45 ,

Sn=400 ,

n=?,common difference = d = ? .

solution : we have ,

Sn = n/2 (t1+tn)

400 = n/2 (5+45)

400×2 = n ( 50 )

800 = 50n

n = 800/50

n= 16.

now,

t16=a+(n-1)d

45=5+(16-1)d

45-5=15d

40=15d

d = 40/15

d = 8/3

the number of terms = 16

common difference = 8/3.