selected solve Answer & explanation by AI To complete part (b), we need to use the generalization from part (a): the sum of the terms is 11 n 2 11n 2 . Find n n for the Sequence Given the sequence: 11 , 33 , 55 , 77 , ... , 143 11,33,55,77,...,143. Identify the Pattern: Each term increases by 22: 33 11 = 22 3311=22, 55 33 = 22 5533=22, etc. Find the Number of Terms, n n: The sequence is arithmetic with the first term a 1 = 11 a 1 =11 and common difference d = 22 d=22. The general formula for the n n-th term of an arithmetic sequence is: a n = a 1 + ( n 1 ) d a n =a 1 +(n1)d Given a n = 143 a n =143: 143 = 11 + ( n 1 ) 22 143=11+(n1)22 Solving for n n: 143 11 = ( n 1 ) 22 14311=(n1)22 132 = ( n 1 ) 22 132=(n1)22 n 1 = 132 22 = 6 n1= 22 132 =6 n = 7 n=7 Calculate the Sum Using the general formula 11 n 2 11n 2 : Sum = 11 n 2 = 11 7 2 = 11 49 = 539 Sum=11n 2 =117 2 =1149=539 The sum of the sequence is 539 539. 12345 Sources 1 1. Arithmetic Sequence A. General Term A sequence is arithmetic if the differences between consecutive terms are the same. So, the sequence a 1 , a 2 , a 3 , a 4 ,., a n1 , a n ,. is arithmetic if there is a number d such that a 2 a 1 = a 3 a 2 = a 4 Arithmetic-Geometric-Sequence_NU-Hand-Outs (1).pdf 2 1|Page SEQUENCE We encounter sequences at the very beginning of our mathematical experience. The list of even numbers 2, 4, 6, 8, 10, . and the list of odd numbers