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

 

G_n = G₁r^n-1;

 

G₅ = G₁r^5-1;

 

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 Log_x7 = ¹/4

 

solution

 

Log_x7 = ¹/4

 

7 = x^1/4 .         [changing logarithmic form into exponential form]

 

(7)⁴= (x^1/4)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 Log_c2 = ¹/7