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

Question

tabuordy · Accepted Answer

Formula to find the nth term of an arithmetic sequence is
$a_{n} = a_{1} + d (n - 1)$
$a_{2} - a_{1} = - 18 - 2 = - 20$
$a_{3} - a_{2} = - 38 - (- 18) = - 38 + 18 = - 20$

Common difference $= d = - 20$
$a_{n} = a_{1} + d (n - 1)$
$a_{55} = 2 + (- 20) (55 - 1)$
$a_{55} = 2 + (- 20) (54)$
$a_{55} = 2 - 1080$
$a_{55} = - 1078$
The 55th term of an arithmetic sequence is -1078.

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

madeleinejames20 · Accepted Answer

To find the 55th term of an arithmetic sequence, we can use the formula:

a_{n} = a_{1} + (n - 1) d

where

a_{n}

is the

n

th term,

a_{1}

is the first term,

n

is the term number, and

d

is the common difference.
In this case, the first term,

a_{1}

, is 2, and the common difference,

d

, can be found by subtracting the second term from the first term:

d = a_{2} - a_{1} = (- 18) - 2 = - 20

Substituting the values into the formula, we have:

a_{55} = 2 + (55 - 1) (- 20)

Now, let's calculate the 55th term:

a_{55} = 2 + (54) (- 20) = 2 - 1080 = - 1078

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

- 1078

.

Nick Camelot · Accepted Answer

Answer:−1078Explanation:Given:an=a1+(n−1)d,where an is the nth term, a1 is the first term, n is the position of the term we want to find, and d is the common difference between consecutive terms.In this case, the first term a1 is 2, and the common difference d can be found by subtracting the second term from the first term:d=−18−2=−20.Now we can substitute the values into the formula to find the 55th term:a55=2+(55−1)(−20).Simplifying the expression inside the parentheses:a55=2+54(−20).Multiplying:a55=2−1080.Finally, performing the subtraction:a55=−1078.Therefore, the 55th term of the arithmetic sequence 2,−18,−38 is −1078.

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

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