SEQUENCE AND SERIES A13

Find the number of terms in the following geometric progression 5+10+20+40+ … + 1280

Solution

G₁=5, G_n=1280, r=2.

G_n = G₁r^n-1;

1280 = 5 x 2^n-1;

1280 = 5 x 2^n-1;       (Divide by 5 on both sides)

   5         5

256 = 2^n-1;

256 = 2ⁿ x 2^-1;

256 = 2ⁿ x ¹/2;

256  =  2ⁿ;  (Divide by ¹/2 on both sides)

  ¹/2      

512 =  2ⁿ;     (512 = 2x2x2x2x2x2x2x2x2)

2⁹ =  2ⁿ;

9 = n

There are 9 terms in a Geometrical Progression.

STATISTICS A6

In Kiswahili test the following marks were recorded.

marks	10-19	20-29	30-39	40-49	50-59	60-69
No. of students	2	4	9	7	5	3

Calculate the mean.

Solution

Here you are required to produce the frequency distribution table.

Class interval	Class mark (x)	Frequency(f)	fx
10-19	14.5	2	29
20-29	24.5	4	98
30-39	34.5	9	310.5
40-49	44.5	7	311.5
50-59	54.5	5	272.5
60-69	64.5	3	193.5
		∑f = 30	∑fx = 1215

Mean = ∑fx

               ∑f

Mean = 1215

                 30

Mean =  40.5

         

Hence Mean =  40.5

SEQUENCE AND SERIES A12

The first term of an AP is 18 and the last term is 100.If the arithmetic progression consists of 20 terms, calculate the sum of all the terms.

Solution

A₁ = 18, n=20, A_n = 100

S_n = n(A₁ + A_n)

       2

S₂₀ = 20(18 + 100)

         2

S₂₀ = 10 x 118

S₂₀ = 1180

Hence the sum of all 20 terms is 1180.

PROBABILITY A5

RADIANS 7

SEQUENCE AND SERIES A11

The sum of the 1st six terms of a geometrical progression is 189. If the common ratio is 2 find the 1st term.

solution

S₆ = 189 G₁ = ?, r=2, n=6

S_n = G₁(rⁿ-1)/r-1

               

S₆ = G₁(r⁶-1)/ r-1

              

189= G₁(2⁶-1)/2-1

               

189= G₁(64-1)

                  1

189= G₁(63)

                 

189 = 63 G₁

³ 189   =  G₁

   63

G₁ = 3

Hence the 1st term is 3.

STATISTICS A5

The masses of 10 coconuts in kilograms were recorded as follows:

5, 8, 4, 3, 6, 7, 2, 5, 1,  and 1. Calculate the median of these data.

Solution

Arrange the data in order of magnitude starting with the smallest.

1, 1, 2, 3,  4, 5 ,5,  6, 7, 8

There are eight data so far. We get the two data in the middle which are 4 and 5.

Median can be calculated by finding the average of the two middle values.

So, median  = 4+ 5

                         2

                      = 4.5

Hence median is 4.5.

REPEATING DECIMAL A8

RADIANS 6

STATISTICS A4

In Mathematics test the following marks were recorded.

marks	31-40	41-50	51-60	61-70	71-80	81-90
No. of students	5	7	14	10	8	6

Calculate the mean.

Solution

Here you are required to produce the frequency distribution table.

Class interval	Class mark (x)	Frequency(f)	fx
31-40	35.5	5	177.5
41-50	45.5	7	318.5
51-60	55.5	14	777
61-70	65.5	10	655
71-80	75.5	8	604
81-90	85.5	6	513
		∑f = 50	∑fx = 3045

Mean = ∑fx

               ∑f

Mean = 3045

               50

Mean =  60.9

         

Hence Mean =  60.9