The first term, a₁, is given as 36 and the common difference, d, is given as -7.
To find the explicit formula for an arithmetic sequence, we can use the formula an = a₁ + (n-1)d.
Substituting the given values into the formula, we have:
36 = 36 + (n-1)(-7)
Simplifying the equation, we get:
36 = 36 - 7n + 7
-7n + 7 = 0
-7n = -7
n = 1
So the term in the sequence we are given corresponds to the first term (n = 1).
To find the first five terms, we can substitute n = 1 to n = 5 into the explicit formula:
a₁ = 36
a₂ = 36 + (2-1)(-7) = 29
a₃ = 36 + (3-1)(-7) = 22
a₄ = 36 + (4-1)(-7) = 15
a₅ = 36 + (5-1)(-7) = 8
Therefore, the first five terms of the sequence are 36, 29, 22, 15, and 8. The explicit formula for the arithmetic sequence is an = 36 - 7(n-1).
Given a term in an arithmetic sequence and the common difference find the first five terms and the explicit formula.
an=36=-276; d=-7
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