Math Assessment

Math Assessment
1

l. a) Find the sum of 8 terms of these series:
(i) 1+4+7
It is an AP series with AP with a = 1 and d = 3
The sum of n terms of an AP is
Sn = (n/2)[2a+(n-1)d].
Therefore, the sum of 8 terms is
S8 = (8/2)[2*1+(8–1)*3]
= (8/2)[2+7*3]
= (4)(23)
Answer= 92
(ii)l+4+16+.....
an=a1×rn−1
a1= 1
r=4/1=16/4=64/ 16=4
So, sum of 8 terms will be
1*48-1
4-1
= 65536-1
3
Ans= 21845
2

1. b) Find the sum to infinity Of these series:
(i) 10+5+2.5...
= a1 (1-rn) / (1-r)
= infinite series means rn= 0
So, 1-rn = 1
So, S∞ = a1 / (1-r ).
=10/(1-0.5)
=10/0.5
= 20
(i) 1-1/2+1/4...
= a1 (1-rn) / (1-r)
= infinite series means rn= 0
So, 1-rn = 1
So, S∞ = a1 / (1-r ).
=1/(1-(-0.5))
=1/1.5
= 0.667
2 a) Find the coefficient of x3 in the expansion of (l + 3x)5
=Tr+1= 5Cr (1)r (3x)5-3
=put r=3
T3+1=5C3 (1)3 (3x)2
=10 (1) (3x)2
=10 (3x)2
3

2 b) Find the coefficient of x5 in the expansion of (a-2x)7
=Tr+1= 7Cr (a)r (-2x)7-r
=put r=5
T5+1=7C5 (a)5 (-2x)2
=21 (a)5 (-2x)2
=21 a5 (4x2)3
3. Sketch the graph of
a)
y= sin (x-90)
4

y= 1+sin 2x
5

b) y= tan ^ 1/2 x
6