RI Sequences and Series C7A Tut Sect A (Soln)

RAFFLES INSTITUTION H2 Mathematics (9758) 2025 Year 5 ________________________________________________________________ ____________________________________ Tutorial 7A: Sequences and Series Page 1 of 4 Tutorial 7A: Sequences and Series Section A (Basic Questions) 1 Write down the series given by the summation notation, showing the first three terms and the last two terms whenever possible. (a) 8 1 4 4r r r   (b) 30 4 (5 3 ) r r   (c)  15 5 3 j mj   , where m is a constant Solutions (a) 8 1 4 4r r r   88 11 114 4rr rr  111 11 14 ... 1 2 3... 7 8123 78 4        (b) 30 4 (5 3 ) r r   ( 7) ( 10) ( 13) ... ( 82) ( 85)      (c)  15 5 3 j m j   , where m is a constant 3(5) 3(6) 3(7) ... 3(14) 3(15)mmm m m    

Raffles Institution H2 Mathematics 2025 Year 5 _____________________________________________________________________________________________ ____________________________________ Tutorial 7A: Sequences and Series Page 2 of 4 2 For each of the following series, write down the rth term and express the series using the summation notation. (a) 3 6 9 ... 369  (b) ( 4) ( 1) (2) ... (53)   (c) 114 2 1 ... 24  (d) 22 22 22 1234 78 ...2345 89  Solutions (a) 3 6 9 ... 369 3 6 9 ... 3( ) ... 369 r    123 1 (3 ) r r   (b) ( 4) ( 1) (2) ... (53)   20 19 10 ( 4) ( 1) (2) ... (3 7) ... (53) (3 7) or ( 4 3 ) rr r rr              (c) 114 2 1 ... 24  3 3 12 114 2 1 ... 2 ...24 12 or 2 r r r rr         (d) 22 22 22 1234 78 ...2345 89  1 22 22 222 8 1 2 1 1234 78 ...( 1)2345 ( 1 )89 (1 ) (1 ) r r r r r r r          1 2 3 20 43 ( 0 ) 43 ( 1 ) 43 ( 2 ) 43 ( 1 ) 3 7 53 4 3 (19) r u u u ur r u                 1 2 2 3 1 4 14 2 14 2 14 2 r r u u u u          

Raffles Institution H2 Mathematics 2025 Year 5 _____________________________________________________________________________________________ ____________________________________ Tutorial 7A: Sequences and Series Page 3 of 4 3 Justify whether each of the following statements is true or false. (a)  22 1 44 10 1 nn rr rr    (b)  1 111 2 n r nn   (c) 2 2 10 nn rr rr   (d) 33 55 10 nn rr rr   Solutions (a)  22 1 44 10 1 is true because nn rr rr     2 44 4 4 1 21 4 44 4 0 LHS 1 2 ... (2 ) RHS 1 1 2 ... (2 ) n r n r rn rn               (b)  1 111 2 n r nn   is true for n = 1.  1 1For 1, 1 1 is false because2 n r nn n     1 LHS 1 (1) 1RHS 1 LHS2 n r nn nn      (c) 2 2 10 nn rr rr   is true for n = 1. 2 2 10 For 1, is false because nn rr nrr     22 2 2 1 2 2 0 LHS 1 2 ... RHS 0 1 2 ... LHS n r n r rn rn               (d) 33 55 10 is true because nn rr rr   3 55 55 5 1 3 55 5 5 5 5 0 LHS 1 2 3 ... (3 ) RHS 0 1 2 3 ... (3 ) LHS n r n r rn rn             

Raffles Institution H2 Mathematics 2025 Year 5 _____________________________________________________________________________________________ ____________________________________ Tutorial 7A: Sequences and Series Page 4 of 4 4 It is given that 1 52 n n r r un   , where ru is an expression in terms of r. Find the value of (i) 10 1 r r u   (ii) 10 5 r r u   (iii) 10u [(i) 1074 (ii) 1038 (iii) 517] Solutions (i) 10 10 1 5(10) 2 1074r r u    (ii) 10 10 4 51 1 rr r rr r uu u    10 45(10) 2 5(4) 2 1038    (iii) 10 9 10 11 rr rr uu u   10 95(10) 2 5(9) 2 517   