Given:
The sequence is -8, -12, -16.
To find:
The nth and 52th term of the given sequence.
Solution:
We have,
-8, -12, -16
It is an AP because the difference between consecutive terms are equal. Here, first term is -8 and the common difference is
[tex]r=a_2-a_1[/tex]
[tex]r=-12-(-8)[/tex]
[tex]r=-12+8[/tex]
[tex]r=-4[/tex]
The nth term of an AP is
[tex]a_n=a+(n-1)d[/tex]
Where, a is first term and d is common difference.
Putting a=-8 and d=-4, we get
[tex]a_n=-8+(n-1)(-4)[/tex]
[tex]a_n=-8-4n+4[/tex]
[tex]a_n=-4-4n[/tex]
Putting n=52, we get
[tex]a_{52}=-4-4(52)[/tex]
[tex]a_{52}=-4-208[/tex]
[tex]a_{52}=-212[/tex]
Therefore, the equation for the nth term of the given sequence is [tex]a_n=-4-4n[/tex] and the 52nd term of the sequence is -212.
