Question

i still dont understand how this is solved someone explain please..

For each of the sequence of numbers:
 Identify the type of sequence.
 Determine the next two terms of the sequences.
 Describe a rule which can be used to form the sequence.
(a) 81; 108; 144; : : :
(b) 60, 80, 320/3 ; : : :

Answer 1

(a) 81 +27 = 108 108 + 36 = 144 next 144 + 45 = 189 189 + 54 = 243 rule seems to be : add the next number in the table of 9 which is 9,18,27,36,45,54,63,72,81 and so on (b)here the numbers in the sequence have constant ratio of 1.333333 or 4/3 so 60 * 1.3333 = 80 80 * 1.3333 = 320/3 next 320/3* 4/3 = 1280/9 1280/9 * 4/3 = 5120/27

Answer 2

the (b) is called a geometric progression, also known as a geometric sequence with common ratio 4/3

Answer 3

A mother during a hectic day, was convinced by her son that he should
have a weekly allowance that is increased every two weeks. In weeks one and two
he receives 1 cent per week, in weeks three and four he receives 2 cents per week. If
his allowance continues to double every two weeks, how much would his allowance
be in week 20?