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The first term of a sequence is a multiple of 3 The second term of this sequence is 6 less than the first term. The third term is 1/5 of the first term. The difference between the first and the third term is 12.
Work out the values of the first three terms of this sequence.​

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Answer:

First term [tex] = 15[/tex]

Second term [tex] = 9[/tex]

Third term [tex] = 3 [/tex]

Step-by-step explanation:

Given,

First term [tex] = 3x[/tex]

Second term [tex] = 3x - 6[/tex]

Third term [tex] = \frac{1}{5} (3x) = \frac{3x}{5} [/tex]

Also,

[tex]3x - \frac{3x}{5} = 12[/tex]

[tex] \frac{15x}{5} - \frac{3x}{5} = 12[/tex]

[tex] \frac{15x - 3x}{5} = 12[/tex]

[tex]15x - 3x = 12 \times 5[/tex]

[tex]12x = 60[/tex]

[tex]x = \frac{60}{12} [/tex]

[tex]x = 5[/tex]

With the value of [tex]x[/tex], we conclude that the first three terms are as follows:

First term [tex] = 3x = 3×5 = 15[/tex]

Second term [tex] = 3x - 6 = 15 - 6 = 9[/tex]

Third term [tex] = \frac{3x}{5} =\frac{15}{5}= 3 [/tex]

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