Question

Find the first six terms of the sequence. a1 = -4, an = an-1 + 7

Answer 1

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

Answer 2

$a_n=a_{n-1}+7\\\\a_1=-4\\a_2=-4+7=3\\a_3=3+7=10\\a_4=10+7=17\\a_5=17+7=24\\a_6=24+7=31$