Given the first term and the common difference of an arithmetic sequence how do you find the first five terms and explicit formula: a1= -34, d=-10?

1 Answer
Ernest Z.
Jul 17, 2015

The explicit formula for the sequence is color(red)( a_n = -10n-24)an=−10n−24, and the first five terms are color(red)(-34, -44, -54, -64, -74)−34,−44,−54,−64,−74.

Explanation:

We know that the common difference d = -10d=−10.

The general formula for an arithmetic sequence is

a_n = a_1 + (n-1)dan=a1+(n−1)d.

So, for your sequence, the general formula is

a_n = -34 + (n-1)(-10) = -34 -10n+10an=−34+(n−1)(−10)=−34−10n+10

a_n = -10n-24an=−10n−24

a_1 = -34a1=−34

a_2 = -10×2-24 = -20-24 = -44a2=−10×2−24=−20−24=−44

a_3 = -10×3-24 = -30-24 = -54a3=−10×3−24=−30−24=−54

a_4 = -10×4-24 = -40-24 = -64a4=−10×4−24=−40−24=−64

a_5 = -10×5-24 = -50-24 = -74a5=−10×5−24=−50−24=−74

The first five terms are -34, -44, -54, -64, -74−34,−44,−54,−64,−74.

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