Answer:
Step-by-step explanation:
Given that the first difference of a sequence is the arithmetic sequence 1, 3, 5, 7, 9, ....
a) When I term a =1
[tex]a_2 =1+1 =2\\a_3 = 4+5 =9\\a_4 = 9+7 =16\\a_5 =16+9 =25\\a_6=25+11 =36[/tex]
Thus first 6 terms are
1,2,5,12,21,32.....
b) Here [tex]a_1+a_2=5\\a_2-a_1 =3\\-------------\\2a_2=8\\a_2 =4\\a_1 =1[/tex]
[tex]a_2 =1+3 =4\\a_3 = 4+5 =9\\a_4 = 9+7 =16\\a_5 =16+9 =25\\a_6=25+11 =36[/tex]
So sequence would be
3,4,9,16,25, 36,...
c) When 5th term is 28
we have the sequences as
a1, a1+1,a1+1+3, ...a1+1+3+5+7
When 5th term is 28 we have
[tex]a_1 +16 =28\\a_1 =12\\[/tex]
Hence first 6 terms would be
12, 13, 16, 21, 28, 37,...
