Sequences and Series

1. An arithmetic sequence has first term 3 and common difference 5. Find
   (a) the term
   (b) the sum of the first 12 terms.
2. If , where
   find the exact value of

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4. A geometric sequence has first term 54 and term 2 .

After how many terms is the sum of the terms of the sequence greater than of the sum to infinity?

5. In this question you must show detailed reasoning

A car association predicts that a new car will lose approximately of its value each year. Lisa buys a new car. She wants to keep it until its value is less than of its original value.
(a) Using this model, how long will she keep the car?
(b) Suggest a reason why this model is unlikely to be accurate in the long term.
6. When Mirka is 5 years old, her parents start to give her pocket money of 50 p per week. On her birthday each year, her parents increase her pocket money by 50 p .
(a) How much pocket money does Mirka get in the first year?
(b) How much more money in total does Mirka get in the second year than the first year?
After how many complete years is the total amount Mirka has been given more than £1000?
7. At the beginning of each month, Mark puts from his salary into a savings account. At the end of every month, interest is added to his savings at the rate of per month.
(a) Show that the amount of money in Mark’s account at the end of months is given by

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(b) How much does Mark have after 5 years if he saves a month at an interest rate of per month?