Please answer the following questions:

Q10. An arithmetic series has first term a and common difference d. The sum of the first 25 terms of the series is 3500. (a) Show that a + 12d = 140. (3) (b) The fifth term of this series is 100. Find the value of d and the value of a. (4) (c) The nth term of this series is u.. Given that 33 un un find the value of #=1 (3) (Total 10 marks) Q11. (a) Use logarithms to solve the equation 0.8*= 0.05, giving your answer to three decimal places. (3) (b) An infinite geometric series has common ratio r. The sum to infinity of the series is five times the first term of the series. (i) Show that r = 0.8. (3) (ii) Given that the first term of the series is 20, find the least value of n such that the nth term of the series is less than 1. (3) (Total 9 marks) Page 4 of 5