Edexcel IAL WMA12/01/P2/June/Oct 2020/Q5 (Geometric Series)
Ben is saving for the deposit for a house over a period of 60 months.
Ben saves £100 in the first month and in each subsequent month, he saves £5 more than the previous month, so that he saves £105 in the second month, £110 in the third month, and so on, forming an arithmetic sequence.
Find the amount Ben saves in the 40th month.
(2)
Find the total amount Ben saves over the 60-month period.
(3)
Lina is also saving for a deposit for a house.
Lina saves £600 in the first month and in each subsequent month, she saves £10 less than the previous month, so that she saves £590 in the second month, £580 in the third month, and so on, forming an arithmetic sequence.
Given that, after a months, Lina will have saved exactly £18200 for her deposit,
form an equation in n and show that it can be written as
(3)
Solve the equation in part (c).
(2)
State, with a reason, which of the solutions to the equation in part (c) is not a sensible
value for n.
(1)
SOLUTION
a-
BEN | Month Number | 3 | ||
Term | ||||
Savings | £100 | £105 | £110 |
Since it is the arithmetic sequence, using the nth term formula of it.
Where,
b- To find the total amount Ben saves over 60 months, use the sum formula where
c-
LINA | Month Number | 3 | ||
Term | ||||
Savings | £600 | £590 | £580 |
The amount Lina would have saved is
d- solving the quadratic equation with the help of quadratic formula.
Where,
e- solution 65 isnt the sensible answer because Lina would already be a ble to save the required amount by the end of 56th month, so she doesn’t need to further save. Moreover, on subtituting the value 65 the sum would be -50 as shown below.
Hence, the not sensible answer is 65.
