Helen and Jane both commence new jobs each starting on an annual salary of ( $ 70,000 ). At the start of each new year, Helen receives an annual salary increase of ( $ 2400 ). Let ( $ H_{n} ) represent Helen's annual salary at the start of her ( n )th year of employment. Show that ( H_{n}=2400 n+67600 ). 1b. [1 mark] At the start of solutionspile.com

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Helen and Jane both commence new jobs each starting on an annual salary of  (  $ 70,000  ). At the start of each new year, Helen receives an annual salary increase of  (  $ 2400  ). Let  (  $ H_{n}  ) represent Helen's annual salary at the start of her  ( n  )th year of employment. Show that  ( H_{n}=2400 n+67600  ). 1b. [1 mark] At the start of each new year, Jane receives an annual salary increase of  ( 3  %  ) of her previous year's annual salary. Jane's annual salary,  (  $ J_{n}  ), at the start of her  ( n  )th year of employment is given by  ( J_{n}=  )  ( 70000(1.03)^{n-1}  ) Given that  ( J_{n}  ) follows a geometric sequence, state the value of the common ratio,  ( r  ). 1c. [3 marks] At the start of year  ( N  ), Jane's annual salary exceeds Helen's annual salary for the first time. Find the value of  ( N  ). 1d. [2 marks] For the value of  ( N  ) found in part (c) (i), state Helen's annual salary and Jane's annual salary, correct to the nearest dollar. 1e. [4 marks] Find Jane's total earnings at the start of her 10 th year of employment. Give your answer correct to the nearest dollar. solutionspile.com

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