Mathelaureate IBDP Mathematics Topic β1: Algebra Sequence and Series Practice problems 1 2 3 4 5 The general term of an arithmetic sequence is π’π = 3π + 4. [a] Find the first 4 terms of the sequence. [2] [b] Find the 50th term of the sequence. [3] The general term of an arithmetic sequence is π’π = 11 β 4π . [a] Find the first term and common difference [2] [b] Find the 20th term [3] Consider the sequence 2, 6, 10, 14, . . . . . . . [a] Show that itβs an arithmetic sequence [b] Find the next three terms [c] Find the expression for the nth term of the sequence [d] Hence find the 15th term of the sequence [1] [1] [2] [2] Consider the arithmetic sequence 20, 17, 14, 11, . . . . . . [a] Find the common difference [1] [b] Find the 10th term of the sequence. [2] [c] Given that π’π = β37 , find π. [3] Given that 16th term in an arithmetic sequence is 44 and the common difference is 3. [a] Find the first 4 terms of the sequence. [2] [b] Find the 51st term of the sequence. [3] [c] Find the sum of first 20 terms of the sequence. [3] IBDP Math/ Sequence & series / D. J Page 1 of 4 www.mathelaureate.com Mathelaureate 6 In an arithmetic sequence π’10 = 43 and π’33 = 204 find the first term and the common difference. [5] 7 Find the sum of the series 11 + 18 + 25+ . . . . . . . . . . . . + 74 [5] 8 In an arithmetic sequence the first term is 3 and the 25th term is 51. Find the sum of the first 30 terms of the sequence. [6] 9 In an arithmetic sequence the first term is 16, nth term (π’π ) is 81 and the sum of the first π terms (ππ ) is 679. Find the number of terms (π) in the sequence. [6] 10 In an arithmetic sequence 10th term is 109 and 38th term is 389. [a] Find the first term and the common difference. [3] [b] Find the 20th term of the sequence. [3] 11 In an arithmetic sequence π’14 = β52 and π’40 = β156. Find the sum up to 50 terms of the series. [6] 12 In an arithmetic sequence π’1 = β38 , π’π = β478 and ππ = β11610 , find the number of terms π. [6] 13 Express the following sigma notation in expanded (series) form. Do not find the sum. 10 [π] [π ] 20 β(3π + 5) [π] β(9 β 10π) π=1 π=1 15 10 β(3π β 5) [π] π=1 IBDP Math/ Sequence & series / D. J 9 5π β( β ) 4 2 [4] π=1 Page 2 of 4 www.mathelaureate.com Mathelaureate 14 Evaluate the sum of the following expressions. 10 [π] 50 [π] β(2π + 7) π=1 15 β(4π β 3) [6] π=1 Find the missing terms in each of the following geometric sequence. [a] _____ , 1 , _______ , 9 [b] _____ , 4 , _______ , 36 [c] 3, _____ , _____ , _____ , 48 [d] 2 , _____ ,_____ ,_____ ¸162 [4] 16 17 In a geometric sequence the first term is 5 and the common ratio is 2. [a] Find the 10th term. [2] [b] Find the sum up to 7 terms. [3] First three terms of a sequence are 4 , 8 , 16 [a] show that it is a geometric sequence [b] Find the next three terms [c] Find the general term expression [d] hence find the 10th term of the sequence 18 The first three terms of a geometric sequence are 250, 50, 10 . . . [a] Show that sum up to infinity exist for this sequence [b] Find the next three terms [c] Find the sum up to infinity of the sequence. 19 The first three terms of a series are β27 + 9 β 3+ . . . . . . . . . .. [a] Show that this is a infinite geometric series [b] Find the 7th term of the series [c] Find the sum of first 7 terms of the series [d] Find the sum of the first 10 terms of the series [e] Find the sum up to infinity of the series. IBDP Math/ Sequence & series / D. J Page 3 of 4 www.mathelaureate.com Mathelaureate 20 In a geometric sequence π’1 = 3 , and π’4 = 375. [a] Find the common ration β r β . [b] Find the 8th term of the sequence [c] Find π7 . IBDP Math/ Sequence & series / D. J Page 4 of 4 www.mathelaureate.com
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