Answer:
The nth term of AP is calculated as [tex]a_n=9n-24[/tex]
Step-by-step explanation:
Given : An arithmetic sequence -15, -6, 3, 12, ...
We have to find the nth term of the given arithmetic sequence -15, -6, 3, 12,..
Consider the given arithmetic sequence -15, -6, 3, 12, ...
Here, [tex]a_1=-15\ ,a_2=-6\ ,a_3=3[/tex]
We first find the common difference (d)
Common difference can be find by finding difference between two successive terms of given arithmetic sequence.
[tex]a_2-a_1=-6+15=9\\\\ a_3-a_2=3+6=9[/tex]
Thus, common difference of given AP is 9
Thus, The equation to find the nth term of AP is calculated as,
[tex]a_n=a+(n-1)d[/tex]
Substitute a = -15 , d = 9 , we get,
[tex]a_n=-15+(n-1)9\\\\ a_n=-15+9n-9\\\\ a_n=9n-24[/tex]
Thus, the nth term of AP is calculated as [tex]a_n=9n-24[/tex]
Answer:
aₙ = 9n - 24 is the nth term of arithmetic sequence.
Step-by-step explanation:
we have given arithmetic sequence:
-15, -6, 3, 12, ...
we have to find the nth term of the arithmetic sequence.
consider the given arithmetic sequence -15, -6, 3, 12, ...
here a₁= -15 , a₂= -6 ,a₃ = 3,......
we first find the common difference between consecutive terms (d).
common difference can be find by finding difference between two successive terms of give arithmetic sequence -15, -6, 3, 12, ...
a₂ - a₁ =( - 6 ) - ( - 15) = 9
a₃ - a₂ = ( 3 ) - ( - 6 ) = 9
hence common difference of given arithmetic sequence is 9.
thus the formula to find the nth term of arithmetic sequence is given below
aₙ = a +( n - 1 ) d
putting a = -15 , d = 9 we get
aₙ = ( -15 ) + ( n-1 ) 9
aₙ = - 15 + 9n - 9
aₙ = 9n - 24 this is the nth term of arithmetic sequence.
