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Algebra Level 2 Test 4

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Question 1
Given that 1 +2+3+4……+10 = 55 , then what will be the sum of 6 + 12 + 18 + 24 …… + 60 ?
A
300
B
500
C
330
D
306
Question 1 Explanation: 
We are given the equation 6 + 12 + 18 + 24 …… + 60
We can write this as 6 (1 +2+3+4……+10) = 6 x 55 = 330
Hence the right option is (a)
Question 2
If 12 +22+32+42….. +202 = 2870, then what will be the value of 22 + 42+ 62+……………………..+402?
A
11480
B
11580
C
11680
D
11780
Question 2 Explanation: 
We are given by the series 12
+22+32+42….. +202 =2870
We need to figure out: 22 + 42+ 62+……………………..+402
This equation can be written as
22 x (12 +22+32+42….. +202) = 4 x 2870 = 11480
Question 3
The value of 1 – 1/20 + 1/202 – 1/203 + ….. , correct up to 5 place of decimal is
A
1.05
B
0.95238
C
0.95239
D
10.5
Question 3 Explanation: 
The series which is given is a Geometric Progression series
So we know the sum of an infinite G.P.= when r<1 then sum will be = a/1-r
Where a is the first term and r is the common ratio
So the sum of the series = a/1-r = [1/{1-(-1/20)}]= 20/21 = 0.95238
Question 4
If the third term of a G.P. is 3 , then the product of first five terms of G.P. is
A
81
B
49
C
342
D
243
Question 4 Explanation: 
Let the G.P. = a/r2, a/r, a, ar, ar2
Given that the third term is 3
So the series will become
= 3/r2 , 3/r , 3 , 3r, 3r2
= product of all of these = 243
Question 5
If in a pair of fraction, the first fraction is twice the second fraction and the product of the two fraction is 2/25. What will be the value of the fraction?
A
1/5
B
2/5
C
1/25
D
2/25
Question 5 Explanation: 
We are told that the first fraction is twice the second fraction
So let the second fraction first = 2p/q
Now the first fraction will be = p/q
On multiplication of two of the fractions we get p/q = 1/5
Therefore first fraction will be = 2 x 1/5 = 2/5
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