Find the 55th term of the arithmetic sequence 2, -18, -38, ,−18,−

The 55th term of the arithmetic sequence 2, -18, -38, ...is - 1078

Given:

2, -18, -38, ...

first term, a = 2

common difference, d = difference between consecutive terms

= -18 - 2 = -38 - (-18)

= -20

d = -20

nth term = a + (n - 1)d

where,

n = number of terms

55th term = a + (n - 1)d

= 2 + (55 - 1)-20

= 2 + (54) -20

= 2 + (- 1080)

= 2 - 1080

= -1078

Therefore, 55th term of the arithmetic sequence 2, -18, -38, ...is - 1078

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-1078

Step-by-step explanation:

Notice that each new term of 2, -18, -38 is found by subtracting 20 from the previous term.

Note that a(2) = first term - 20, or

                a(2) =        2       -20(2-1), or

                a(3) =        2       -20(3-1)   =    2 -20(2) = 2 - 40 = -38 (this is right)

So the nth term is a(n) = 2 - 20(n-1)

and the 55th term is a(55) = 2 - 20(55-1) = 2 - 20(54) = -1078

The 55th term is -1078.

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