The position and terms of the arithmetic sequence are as follows:
- position = 6, term = -10
- position = 8, term = -14
- position = 11, term = -20
- position = 19, term = -36
How to solve arithmetic sequence?
Arithmetic sequence formula is represented as follows:
aₙ = a + (n - 1)d
where
- a = first term
- d = common difference
- n = number of terms
Therefore, the position is the number of terms and the term is the nth term.
Hence,
a = 0
Let's find the common difference using the nth term -48.
- 48 = 0 + (25 - 1)d
-48 = 25d - d
-48 = 24d
d = - 2
Hence, let's use the first term and common difference to find the position or terms of the arithmetic sequence.
Therefore,
-10 = 0 + (n - 1)-2
-10 = 0 - 2n + 2
-10 - 2 = - 2n
-12 = -2n
n = 6
a₈ = 0 + 7(-2)
a₈ = - 14
-20 = 0 + (n - 1)-2
-20 = 0 - 2n + 2
-20 - 2 = -2n
-22 = -2n
n = 11
a₁₉ = 0 + 18(-2)
a₁₉ = 0 - 36
a₁₉ = -36
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