Get premium membership and access questions with answers, video lessons as well as revision papers.
a) 4,12,36, ...............
Common ratio
r = -$\frac{12}{4}$ = -3
nth term of a G.P = arn-1
6th term = ar6-1
= 4(-3)5 = 4(-243)
= -972
b) Sn = a$\frac{1-r^n}{1-r}$
S8 = 4$\frac{(1-(-3)^8)}{1-(-3)}$
S8 = -6 560
c) 12th term
= 5 times (second term)
a + 11d = 5(a+d)
a + 11d = 5a + 5d
6d = 4a therefor a = $\frac{6d}{4}$
120 = $\frac{10}{2}(2a+9d)$
240 = 20a + 90d
240 = $\frac{120d}{4}$ + 90d
240 = 30d + 90d
240 = 120d d = 2
But a = $\frac{6d}{4}$
a = $\frac{6\times 2}{4}\; = \frac{12}{4}\; = 3$
the first term is 3 and the common difference is 2
johnmulu answered the question on March 8, 2017 at 14:01
- The positions of two towns X and Y are given to the nearest degree as X(45oN, 10oW) and Y(45oN, 70oW). Find
(Solved)
The positions of two towns X and Y are given to the nearest degree as X(45oN, 10oW) and Y(45oN, 70oW). Find
a) The difference in longitude
b) The distance between the towns in
ii) Nautical miles (1nm = 1.85 km and R = 6370 km)
ii) the local time at Y is 2.00 p.m
Date posted: March 8, 2017. Answers (1)
- Simplify: $\frac{3a^2\;-48}{48\;-24a + 3a^2}$(Solved)
Simplify: $\frac{3a^2\;-48}{48\;-24a + 3a^2}$
Date posted: March 8, 2017. Answers (1)
- Two points P and Q lies on latitude 65 2S. Their longitudes are 96 2E and 84 2W respectively. Find the distance between them in km. Take R = 6370 km and $\pi = 3.142$(Solved)
Two points P and Q lies on latitude 65 2S. Their longitudes are 96 2E and 84 2W respectively. Find the distance between them in km. Take R = 6370 km and $\pi = 3.142$
Date posted: March 8, 2017. Answers (1)
- Calculate the area enclosed between the curve y = 6x - x2 x –axis and the lines x = 1 and x = 5 using...(Solved)
Calculate the area enclosed between the curve y = 6x - x2 x –axis and the lines x = 1 and x = 5 using the mid-ordinate rule with four strips
Date posted: March 8, 2017. Answers (1)
- Calculate the area enclosed between the curve y = 6x - x2, x - axis and the lines x = 1 and x = 5 using the mid-ordinate rule with four strips(Solved)
Calculate the area enclosed between the curve y = 6x - x2, x - axis and the lines x = 1 and x = 5 using the mid-ordinate rule with four strips
Date posted: March 8, 2017. Answers (1)
- Intersection point of the lines of equations 2x – 3y = -29 and circle whose radius is 5 units. Find the equation of the circle(Solved)
Intersection point of the lines of equations 2x – 3y = -29 and circle whose radius is 5 units. Find the equation of the circle
Date posted: March 8, 2017. Answers (1)
- Given (1 – 3x)5
Determine the number of terms in the expansion(Solved)
Given (1 – 3x)5
a) Determine the number of terms in the expansion
b) Expand (1 - 3)5 and use your expansion to estimate (0.97)5 correct to 4 significant figures
Date posted: March 8, 2017. Answers (1)
- Solve the equation
log3(x + 23) - log3(log232) = log3(9 - 2x)(Solved)
Solve the equation
log3(x + 23) - log3(log232) = log3(9 - 2x)
Date posted: March 8, 2017. Answers (1)
- Given that P = 4 + $\sqrt2 $ and that
$\frac{P}{Q}$ = a + b$\sqrt c$ where a, b and c are constants, find the values of a, b and c (Solved)
Given that P = 4 + $\sqrt2 $ and that
$\frac{P}{Q}$ = a + b$\sqrt c$ where a, b and c are constants, find the values of a, b and c
Date posted: March 8, 2017. Answers (1)
- A ship leaves an island (5o, 45oE) and sails due east for 120 hours to another island. The average speed of the ship is 27 knots(Solved)
A ship leaves an island (5o, 45oE) and sails due east for 120 hours to another island. The average speed of the ship is 27 knots
a) Calculate the distance between the two islands
i) in nautical miles
ii) in kilometres
b) Calculate the speed of the ship in kilometres per hour
c) Find the position of the second island. (Take 1 nm to be 1.853 km and the radius of the earth to be 6370 km)
Date posted: March 8, 2017. Answers (1)
- A stone is thrown vertically upwards such that its height is S metres above the ground after t seconds is given by s = 40t - 10t2.
Find(Solved)
A stone is thrown vertically upwards such that its height is S metres above the ground after t seconds is given by s = 40t - 10t2.
Find
i) The height above the ground after 2 seconds
ii) The velocity after 1 second
iii) The instant at which the stone is 30 m high
Date posted: March 8, 2017. Answers (1)
- A solid cone of height 12 cm and radius 9 cm is recast into a solid sphere. Calculate the surface area of the sphere(Solved)
A solid cone of height 12 cm and radius 9 cm is recast into a solid sphere. Calculate the surface area of the sphere
Date posted: March 8, 2017. Answers (1)
- Solve the simultaneous equations
x2 + y2 = 26
x + y = 4(Solved)
Solve the simultaneous equations
x2 + y2 = 26
x + y = 4
Date posted: March 8, 2017. Answers (1)
- A G.P has third term 24 and sixth term 192. Determine the first term and the common ratio(Solved)
A G.P has third term 24 and sixth term 192. Determine the first term and the common ratio
Date posted: March 8, 2017. Answers (1)
- Differentiate y = (x + 2)(x - 1) with respect x (Solved)
Differentiate y = (x + 2)(x - 1) with respect x
Date posted: March 8, 2017. Answers (1)
- Determine the centre and radius of a circle given by the equation
$2x^2\;+\;2y^2\;-\;12\;=\;4x\;-\;12y$(Solved)
Determine the centre and radius of a circle given by the equation
$2x^2\;+\;2y^2\;-\;12\;=\;4x\;-\;12y$
Date posted: March 8, 2017. Answers (1)
- Solve for y given that
$log_2(2y\; + \;3)-\;2\; = log_2(y - 2)$
(Solved)
Solve for y given that
$log_2(2y\; + \;3)-\;2\; = log_2(y - 2)$
Date posted: March 8, 2017. Answers (1)
- Evaluate (3 - $\sqrt7$)(3 + $\sqrt7$) hence simplify
$\frac{2}{3\; -\sqrt7}$ - $\frac{2}{3\; +\sqrt7}$(Solved)
Evaluate (3 - $\sqrt7$)(3 + $\sqrt7$) hence simplify
$\frac{2}{3\; -\sqrt7}$ - $\frac{2}{3\; +\sqrt7}$
Date posted: March 7, 2017. Answers (1)
- The sides of triangles were measured and recorded as 8.4 cm, 10.5 cm and 15.3 cm. Calculate the percentage error in perimeter (Solved)
The sides of triangles were measured and recorded as 8.4 cm, 10.5 cm and 15.3 cm. Calculate the percentage error in perimeter correct to 2 decimal places
Date posted: March 7, 2017. Answers (1)
- The equation of a curve is
y = 3x2 -4x + 1, Find the gradient function of the curve and its value when x = 2(Solved)
The equation of a curve is
y = 3x2 -4x + 1
a) Find the gradient function of the curve and its value when x = 2
b) Determine the equation of the tangent to the curve at(2,5)
Date posted: March 7, 2017. Answers (1)