Seq Series BMQ Soln (RVHS)

Ch 2 Sequences and Series (Solutions to Tutorial & Assignment) RIVER VALLEY HIGH SCHOOL 11 Tutorial 2B: Sequences and Series (Part II) – AP & GP, ΣΣ ΣΣ Notation, MOD Basic Mastery Questions 1. Find the sum of all the even numbers from 20 to 100 inclusive. 2. Find the number of terms that must be taken for the sum of t he arithmetic series …+++ 20 16 12 to be equal to 672. 3. The rth term of an arithmetic progression is ) 41 ( r+ . Find, in terms of n, the sum of the first n terms of the progression.

Ch 2 Sequences and Series (Solutions to Tutorial & Assignment) RIVER VALLEY HIGH SCHOOL 12 4. Find the number of terms that must be taken for the sum of t he geometric series …+++ 12 24 48 to be equal to 4 195 . 5. [N1987/I/11 ] Find ( ) 0 2 1 2 n r n r = + −  in terms of n. ( ) ( ) ( )( ) ( ) ( )( ) ( ) ( ) ( ) ( ) 0 0 0 2 2 1 2 2 1 2 12 1 1 2 2 2 1 1 1 1 2 1 1 n n n r r r n r n r n n n n n n n n n n n n = = = + − = + − += + + − = + + − + = + + − = +    6. The nth term of a series is nn 32 2 +− . Find the sum of the first N terms.

Ch 2 Sequences and Series (Solutions to Tutorial & Assignment) RIVER VALLEY HIGH SCHOOL 13 7. Express 1 (2 1)(2 1) n n − + in partial fractions and use the method of differen ces to find 1 1 (2 1)(2 1) N n n n = − +  , giving your answer in terms of N.