The first three terms of an arithmetic series are x-1, 5x-3, 4x+5, how do you find the sixth term?

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The first three terms of an arithmetic series are x-1, 5x-3, 4x+5, how do you find the sixth term?

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Answer 1 · 2016-02-07T00:08:45

The sixth term is $31$ $31$

Explanation:

It should be

$5 x - 3 - (x - 1) = 4 x + 5 - (5 x - 3) \Rightarrow 4 x - 2 = 8 - x \Rightarrow 5 x = 10 \Rightarrow x = 2$ $5x-3-(x-1)=4x+5-(5x-3)=>4x-2=8-x=>5x=10=>x=2$

Hence the first three terms are $2 - 1 = 1$ $2-1=1$ , $5 \cdot 2 - 3 = 7$ $5*2-3=7$ , $4 \cdot 2 + 5 = 13$ $4*2+5=13$

So it is an arithmetic series with first term $a_{1} = 1$ $a_1=1$ and ratio $r = 6$ $r=6$

hence

$a_{6} = a_{1} + (6 - 1) \cdot 6 = 1 + 30 = 31$ $a_6=a_1+(6-1)*6=1+30=31$

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The first three terms of an arithmetic series are x-1, 5x-3, 4x+5, how do you find the sixth term?

1 Answer

Explanation:

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