- A company offers two salary schemes for a 10 -year period, Year 1 to Year 10 inclusive.
Scheme 1: Salary in Year 1 is \(\pounds P\).
Salary increases by \(\pounds ( 2 T )\) each year, forming an arithmetic sequence.
Scheme 2: Salary in Year 1 is \(\pounds ( P + 1800 )\).
Salary increases by \(\pounds T\) each year, forming an arithmetic sequence.
- Show that the total earned under Salary Scheme 1 for the 10-year period is
$$\pounds ( 10 P + 90 T )$$
For the 10-year period, the total earned is the same for both salary schemes.
- Find the value of \(T\).
For this value of \(T\), the salary in Year 10 under Salary Scheme 2 is \(\pounds 29850\)
- Find the value of \(P\).