Standard +0.3 Part (a) requires setting up equations using arithmetic sequence formula and the geometric sequence condition (middle term squared equals product of outer terms), then solving a quadratic - a standard multi-step problem. Part (b) involves straightforward arithmetic series summation with a real-world context. Both parts are routine applications of formulas with no novel insight required, making this slightly easier than average.
a) The \(3 ^ { \text {rd } } , 19 ^ { \text {th } }\) and \(67 ^ { \text {th } }\) terms of an arithmetic sequence form a geometric sequence. Given that the arithmetic sequence is increasing and that the first term is 3 , find the common difference of the arithmetic sequence.
b) A firm has 100 employees on a particular Monday. The next day it adds 12 employees onto its staff and continues to do so on every successive working day, from Monday to Friday.
i) Find the number of employees at the end of the \(8 { } ^ { \text {th } }\) week.
ii) Each employee is paid \(\pounds 55\) per working day. Determine the total wage bill for the 8 week period.
a) The $3 ^ { \text {rd } } , 19 ^ { \text {th } }$ and $67 ^ { \text {th } }$ terms of an arithmetic sequence form a geometric sequence. Given that the arithmetic sequence is increasing and that the first term is 3 , find the common difference of the arithmetic sequence.
b) A firm has 100 employees on a particular Monday. The next day it adds 12 employees onto its staff and continues to do so on every successive working day, from Monday to Friday.\\
i) Find the number of employees at the end of the $8 { } ^ { \text {th } }$ week.\\
ii) Each employee is paid $\pounds 55$ per working day. Determine the total wage bill for the 8 week period.
\hfill \mbox{\textit{WJEC Unit 3 2019 Q8}}