RI Sequences and Series C7A Add Prac (Qn)

RAFFLES INSTITUTION H2 Mathematics (9758) 2025 Year 5 ______________________________________________________________ Additional Practice Questions for Chapter 7A: Sequences and Series Page 1 of 2 Additional Practice Questions for Chapter 7A: Sequences and Series 1 Evaluate the following sum. (a)  1 35 n rn r    (b) 2 1 () ( 1 ) n rn rn r   (c)  11 1 2r r r   [You may use the result 1 (1 )2 n r nrn   and 2 1 1 (1 ) ( 21 )6 n r rn n n   ] 2 Given that find, in terms of a, 2 37 (2 ) a r r   , where a is an integer and a  37. [3] 3 Given that 1 (1 )2 n r nrn   and 2 1 1 (1 ) ( 21 )6 n r rn n n   , show that 3 1 3( 1 ) n r rr n n   . [ 3 ] Hence find  2 1 (1 ) 3 (1 ) n rn nr rr    , simplifying your answer. [3] 4 Using 1 (1 )2 n r nrn   , find  100 50 ln 2 3 r r  , leaving your answer in the form ln 2 ln 3,AB  where A and B are constants to be found. [5] 5 (a) The sum, nS , of the first n terms of a sequence 123, , , . . .uuu is given by 1 2 375 5 n n nS   . Show that 1 3 5 n nuk    , where k is a constant to be determined. Find S . [4] (b) Another sequence of numbers 123, , , . . .vvv is such that 1 2 21 n i i nv n   . Find the exact value of 11 i i v    . [3] 2 1 (1 ) ( 21 ) ,6 n r nrn n   

Raffles Institution H2 Mathematics 2025 Year 5 _____________________________________________________________________________________________ _______________________________________________________________ Additional Practice Questions for Chapter 7A: Sequences and Series Page 2 of 2 6 During a clinical trial, the concentration U, of a specific blood agent is measured at one- hour intervals following the initial administration of the trial drug to a patient. The following readings were obtained 34 5 88, 76 and 70,UU U  where tU denotes the reading t hours after the drug was first administered. It is believed that U satisfies the relationship 1 , 0 ,ttU p qU t   where p and q are constants. (a) Find the values of p and q. [2] (b) Determine the initial concentration of the blood agent when the drug was initially administered. [3] (c) Describe how the concentration beha ves over a long period of time. [1] THE END