Answer:
3, 7, 11, 15, 19, 23, 27,.......
Step-by-step explanation:
Let the first term and the common difference of the AP be a and d respectively.
[tex] a_7 = 27 .....(given) [/tex]
Therefore,
a + (7- 1) d = 27
a + 6d = 27
a = 27 - 6d...... (1)
[tex] a _{12} = 47.....(given)[/tex]
Therefore,
a + (12 - 1) d = 47
a + 11d = 47......(2)
From equations (1) & (2)
27 - 6d + 11d = 47
24 + 5d = 47
5d = 47 - 27
5d = 20
d = 20/5
d = 4
Plug d = 4 in equation (1) we find:
a = 27 - 6*4
a = 27 - 24
a = 3
Therefore,
[tex] a_1 = a = 3[/tex]
[tex] a_2 = a_1 + d= 3 + 4 = 7[/tex]
[tex] a_3 = a_2 + d= 7 + 4 = 11[/tex]
[tex] a_4 = a_3 + d= 11 + 4 = 15[/tex]
[tex] a_5 = a_4 + d= 15 + 4 = 19[/tex]
[tex] a_6 = a_5 + d= 19 + 4 = 23[/tex]
[tex] a_7 = a_6 + d= 23 + 4 = 27[/tex]
Thus, the sequence is: 3, 7, 11, 15, 19, 23, 27,.......
