Question:
Write the first five terms of the arithmetic sequence, [tex]a_1 = 3[/tex]; [tex]d = 4[/tex]
Solution/s:
General term formula for arithmetic sequence:
[tex] a_n = a_1 + (n - 1)d [/tex]
Given [tex]a_1 = 3[/tex] and [tex]d = 4[/tex], substitute:
[tex] a_n = a_1 + (n - 1)d [/tex]
[tex] a_n = (3) + (n - 1)(4) [/tex]
[tex] a_n = 3 + 4n - 4 [/tex]
[tex] a_n = 4n - 1 [/tex]
Using [tex] a_n = 4n - 1 [/tex], find the first 5 terms:
Given already the first term [tex] a_1 = 3 [/tex], we just need to find [tex] a_2 [/tex] to [tex] a_5 [/tex].
Second term:
[tex] a_{(2)} = 4(2) - 1 [/tex]
[tex] a_2 = 8 - 1 [/tex]
[tex] a_2 = 7 [/tex]
Third term:
[tex] a_{(3)} = 4(3) - 1 [/tex]
[tex] a_3 = 12 - 1 [/tex]
[tex] a_3 = 11 [/tex]
Fourth term:
[tex] a_{(4)} = 4(4) - 1 [/tex]
[tex] a_4 = 16 - 1 [/tex]
[tex] a_4 = 15 [/tex]
Fifth term:
[tex] a_{(5)} = 4(5) - 1 [/tex]
[tex] a_5 = 20 - 1 [/tex]
[tex] a_5 = 19 [/tex]
The first 5 terms are [tex] 3, 7, 11, 15, 19 [/tex]