The 61st term of sequence is -972
Solution:
Given arithmetic sequence is:
-12, -28, -44, ..
Let us find the common difference between the successive term and its previous term
-28 - (-12) = -28 + 12 = -16
-44 - (-28) = -44 + 28 = -16
Thus the difference between the terms remains constant
This is a arithmetic sequence
The nth term of arithmetic sequence is given by formula:
[tex]a_n = a_1 + (n-1)d[/tex]
Where,
[tex]a_n[/tex] is the nth term of sequence
[tex]a_1[/tex] is the first term of sequence
d is the common difference between terms
In given sequence, -12, -28, -44
[tex]a_1 = -12\\\\d = -16[/tex]
Substituting the values in formula,
[tex]a_n = -12+(n-1)(-16)\\\\a_n = -12 -16n + 16\\\\a_n = 4-16n[/tex]
To find the 61st term , substitute n = 61
[tex]a_{61} = 4 - 16 \times 61\\\\a_{61} = 4 - 976\\\\a_{61} = -972[/tex]
Thus, the 61st term of sequence is -972
