Answer:
first six terms are -4, 3, 10, 17, 24 ,31
Step-by-step explanation:
The given first term and recurrence relation is [tex]a_1 = -4, \; a_n = a_{n-1} +7[/tex]
we need to find first six term of this recurrence relation
[tex]a_1 = -4[/tex]
put n=2 in [tex]a_n = a_{n-1} +7[/tex]
[tex]a_2 = a_{2-1} +7[/tex]
[tex]a_2 = a_1 +7[/tex]
since, [tex]a_1 = -4[/tex]
[tex]a_2 = -4 +7[/tex]
[tex]a_2 = 3[/tex]
similarly,
for n=3
[tex]a_3 = a_{3-1} +7[/tex]
[tex]a_3 = a_2 +7[/tex]
since, [tex]a_2 = 3[/tex]
[tex]a_3 = 3 +7[/tex]
[tex]a_3 = 10[/tex]
For n=4
[tex]a_4 = a_{4-1} +7[/tex]
[tex]a_4 = a_3 +7[/tex]
since, [tex]a_3 = 10[/tex]
[tex]a_4 = 10 +7[/tex]
[tex]a_4 = 17[/tex]
For n=5
[tex]a_5 = a_{5-1} +7[/tex]
[tex]a_5 = a_4 +7[/tex]
since, [tex]a_4 = 17[/tex]
[tex]a_5 = 17 +7[/tex]
[tex]a_5 = 24[/tex]
For n=6
[tex]a_6 = a_{6-1} +7[/tex]
[tex]a_6 = a_5 +7[/tex]
since, [tex]a_5 = 24[/tex]
[tex]a_6 = 24 +7[/tex]
[tex]a_6 = 31[/tex]
Hence, first six terms are -4, 3, 10, 17, 24 ,31
