Find the 61st term of the arithmetic sequence -12, -28, -44, …−12,−28,−44,… Question Find the 61st term of the arithmetic sequence -12, -28, -44, …−12,−28,−44,… in progress 0 Math Melanie 3 months 2022-02-19T05:23:41+00:00 2022-02-19T05:23:41+00:00 2 Answers 0 views 0

## Answers ( )

Answer:-972 is the answer

Step-by-step explanation:The 61st term of sequence is -972Solution: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