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