## 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,…

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3 months 2022-02-19T05:23:41+00:00 2 Answers 0 views 0

Step-by-step explanation:

2. 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:

$$a_n = a_1 + (n-1)d$$

Where,

$$a_n$$ is the nth term of sequence

$$a_1$$ is the first term of sequence

d is the common difference between terms

In given sequence, -12, -28, -44

$$a_1 = -12\\\\d = -16$$

Substituting the values in formula,

$$a_n = -12+(n-1)(-16)\\\\a_n = -12 -16n + 16\\\\a_n = 4-16n$$

To find the 61st term , substitute n = 61

$$a_{61} = 4 – 16 \times 61\\\\a_{61} = 4 – 976\\\\a_{61} = -972$$

Thus, the 61st term of sequence is -972