**3.b.1 - 2016 Q9**

On John’s 10th birthday he received the first of an annual birthday gift of money from his uncle. This first gift was £60 and on each subsequent birthday the gift was £15 more than the year before. The amounts of these gifts form an arithmetic sequence.

A) Show that, immediately after his 12th birthday, the total of these gifts was £225 (1)

B) Find the amount that John received from his uncle as a birthday gift on his 18th birthday (2)

C) Find the total of these birthday gifts that John had received from his uncle up to and including his 21st birthday. (3)

When John had received n of these birthday gifts, the total money that he had received from these gifts was £3375

D) Show that (3)

A) Show that, immediately after his 12th birthday, the total of these gifts was £225 (1)

B) Find the amount that John received from his uncle as a birthday gift on his 18th birthday (2)

C) Find the total of these birthday gifts that John had received from his uncle up to and including his 21st birthday. (3)

When John had received n of these birthday gifts, the total money that he had received from these gifts was £3375

D) Show that (3)

E) Find the value of n, when he had received £3375 in total, and so determine John’s age at this time (3)