Friday 18 October 2024

GP J1

 

The 1st term of a geometric progression is 2 and the 5th term is 512. Find the common ratio.

 

Solution

 

G1=2, G5=512, n=5

 

Gn = G1rn-1;

 

G5 = G1r5-1;

 

G5 = G1r4;

 

512 = 2 x r4;

 

512 = 2r4;

 2       2

 

256 = r4;  Finding the fourth root of 256,

We do prime factorization of 256.

 

2

256

2

128

2

64

2

32

2

16

2

8

2

4

2

2

 

1

 



 

 

 

 

 

 

 

 

 

 


44 = r4;  [equal powers will cancel out]

 

4 = r

 

r = 4

 

 

Hence the common ratio is 4.

 

TRY THIS …………..

The 1st term of a geometric progression is 3 and the 5th term is 9375. Find the common ratio.


GEOMETRY J3

 

The total interior angles of a regular polygon is 5,5800. Find the interior angle.

 

Solution

 

(n-2)1800= Total interior angles.

(n-2)1800 = 5,5800

(n-2)1800 = 5,5800      Dividing by 1800 both sides

    1800              1800

 

(n-2)     =   558279     After canceling by 2

    1                 18 9

 

(n-2)         = 279 93     After canceling by 3

   1                        9  3

 

(n-2)          = 93 31     After canceling by 3 again

    1                      3  1

 

 

(n-2)  = 31

 

n  = 31+2

n = 33

 

i = (n-2)1800

       n            .

 

i = (33-2)1800

        33          

 

i = 31 x1800

        33           

 

i = 31 x 600

        11           

 

 

i = 1860/110

 

Interior angle=1860/110

 

 

TRY THIS……………….

 

 

The total interior angles of a regular polygon is 68400. Find the interior angle.

LOGARITHMS J2

 

Find x if Logx7 = 1/4

 

solution

 

Logx7 = 1/4

 

7 = x1/4 .         [changing logarithmic form into exponential form]

 

(7)4= (x1/4)4 .             [squaring by 4 both sides].

 

(7)4= x.                    [ ¼ ad 4 cancel out]

 

(7x7x7x7) = x

 

 

(49x49) = x

 

2401=x

 

 

Hence x = 2401     

 

 

TRY THIS..................

 

 

Find c if Logc2 = 1/7