General formula a arithmetic progression:
[tex]\boxed { \boxed {T_n= a_1 + (n-1)d}}[/tex]
[tex]\text {Given that } a_ 1 = 7 \text { and } d = 4,[/tex]
[tex]T_n = 7 + 4(n - 1)[/tex]
[tex]T_n = 7 + 4n - 4[/tex]
[tex]T_n = 3 + 4n[/tex]
The nth term for this sequence is :
[tex]\boxed {\boxed {T_n = 3 + 4n}}[/tex]
Find the next 4 terms:
[tex]\text {When n = 4, }T_4 = 3 + 4(4) = 19[/tex]
[tex]\text {When n = 5, }T_5 = 3 + 4(5) = 23[/tex]
[tex]\text {When n = 6, }T_6 = 3 + 4(6) = 27[/tex]
[tex]\text {When n = 7, }T_7 = 3 + 4(7) = 31[/tex]
Answer: The next 4 terms are 29, 23, 37 and 31.
