Algebra Level 2 Test 4

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)

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

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

Let the G.P. = a/r^2, 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

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