SEQUENCE AND SERIES q'S HELP

PLEASE help. Thanx :smile:

The points A(−1, −2), B (7, 2) and C(k, 4), where k is a constant, are the vertices of ABC. Angle ABC is a right angle.

(a) Find the gradient of AB. (2)

(b) Calculate the value of k. (2)

(c) Show that the length of AB may be written in the form p√5, where p is an integer to be found. (3)

(d) Find the exact value of the area of ABC. (3)

(e) Find an equation for the straight line l passing through B and C. Give your answer in the form ax + by + c = 0, where a, b and c are integers. (2)

The line l crosses the x-axis at D and the y-axis at E.

(f ) Calculate the coordinates of the mid-point of DE.

aNOTHER q

Each year, for 40 years, Anne will pay money into a savings scheme. In the first year she pays £500. Her payments then increase by £50 each year, so that she pays £550 in the second year, £600 in the third year, and so on.

(a) Find the amount that Anne will pay in the 40th year. (2)

(b) Find the total amount that Anne will pay in over the 40 years. (2)

Over the same 40 years, Brain will also pay money into the savings scheme. In the first year he
pays in £890 and his payments then increase by £d each year.

Given that Brian and Anne will pay in exactly the same amount over the 40 years.

c) Find the value OF d

Reply 1

singh12

aNOTHER q

Each year, for 40 years, Anne will pay money into a savings scheme. In the first year she pays £500. Her payments then increase by £50 each year, so that she pays £550 in the second year, £600 in the third year, and so on.

(a) Find the amount that Anne will pay in the 40th year. (2)
A is the first term. D is the difference.
A=£500. D=£50 N=40

Un = a+(n-1)d This is the formula to find Nth term.
Un = 500+(n-1)50
= 500+50n-50
Un = 450+50n
U40 = 450+50(40)
U40 = £2450

(b) Find the total amount that Anne will pay in over the 40 years. (2)

Sn=n/2(2a+(n-1)d)
Sn=n/2(1000+(n-1)50
Sn=n/2(1000+50n-50
Sn=n/2(950+50n)
S40=40/2(950+50(40))
S40=£59000

Over the same 40 years, Brain will also pay money into the savings scheme. In the first year he
pays in £890 and his payments then increase by £d each year.

Given that Brian and Anne will pay in exactly the same amount over the 40 years.

c) Find the value OF d

First of all, read the question carefully

S40=59000
59000=40/2(1780+(40-1)d
118000=40(1780+(40-1)d
118000/40 = 1780+39d
2950 = 1780+39d
D = (950-1780)/39
D = 30

Any problem with the answer. plz ask!!!

Thankyou!

What have you done so far? Post your working.

Reply 4

Felix Felicis

13

Original post by BlueSam3

What have you done so far? Post your working.

This thread is 8 years old. :lol:

Reply 5

BlueSam3

17

Well that was one hell of a gravedig.

Reply 6

jess_burton

2

Over the same 40 years, Brain will also pay money into the savings scheme. In the first year he
pays in £890 and his payments then increase by £d each year.

Given that Brian and Anne will pay in exactly the same amount over the 40 years.

c) Find the value OF d

First of all, read the question carefully

S40=59000
59000=40/2(1780+(40-1)d
118000=40(1780+(40-1)d
118000/40 = 1780+39d
2950 = 1780+39d
D = (950-1780)/39
D = 30

I don't understand where you got the 1780 from...

Any problem with the answer. plz ask!!!

Reply 7

hola110100

Original post by Milli

The points A(−1, −2), B (7, 2) and C(k, 4), where k is a constant, are the vertices of ABC. Angle ABC is a right angle.

(a) Find the gradient of AB. (2)

(b) Calculate the value of k. (2)

(c) Show that the length of AB may be written in the form p√5, where p is an integer to be found. (3)

(d) Find the exact value of the area of ABC. (3)

(e) Find an equation for the straight line l passing through B and C. Give your answer in the form ax + by + c = 0, where a, b and c are integers. (2)

The line l crosses the x-axis at D and the y-axis at E.

(f ) Calculate the coordinates of the mid-point of DE.

(a) The gradient of AB is the change in y coordinate/change in x coordinate = 4/8 = 1/2.

(b) AB is perpendicular to BC. From part a, the gradient of AB is 1/2. This means that the gradient of BC is -2, so (4-2)/(k-7) = -2, 2/(k-7)= -2, so k-7=-1 and k=6.

(c) Let F = (7, -2). By Pythagoras, AB = sqrt (AF^2 + BF^2) = sqrt (64+16) = sqrt(80) = 4sqrt(5).

(d) Similarly to part (c), it can be determined that the length of BC = sqrt5. 1/2 base*height = area, so the area is 20.

(e)The gradient of l is -2 and it crosses the y axis at (0,16). Therefore l is of the form y=16-2x, which can be rearranged to 2x+y-16=0.

(f) When x=0, it crosses the y axis (0,16). When y=0, it crosses the x axis (8,0). The midpoint is the arithmetic mean of each coordinate, ie (4,8).

Reply 8

Bevin

12

Original post by jess_burton

Over the same 40 years, Brain will also pay money into the savings scheme. In the first year he
pays in £890 and his payments then increase by £d each year.

Given that Brian and Anne will pay in exactly the same amount over the 40 years.

c) Find the value OF d

First of all, read the question carefully

S40=59000
59000=40/2(1780+(40-1)d
118000=40(1780+(40-1)d
118000/40 = 1780+39d
2950 = 1780+39d
D = (950-1780)/39
D = 30

I don't understand where you got the 1780 from...

Any problem with the answer. plz ask!!!

a=£890
2a=£1780

Reply 9

davros

16

Original post by Bevin

First of all, read the question carefully

S40=59000
59000=40/2(1780+(40-1)d
118000=40(1780+(40-1)d
118000/40 = 1780+39d
2950 = 1780+39d
D = (950-1780)/39
D = 30

I don't understand where you got the 1780 from...

Any problem with the answer. plz ask!!!