Question

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.​

Answer 1

Answer:

First term $= 15$

Second term $= 9$

Third term $= 3$

Step-by-step explanation:

Given,

First term $= 3x$

Second term $= 3x - 6$

Third term $= \frac{1}{5} (3x) = \frac{3x}{5}$

Also,

$3x - \frac{3x}{5} = 12$

$\frac{15x}{5} - \frac{3x}{5} = 12$

$\frac{15x - 3x}{5} = 12$

$15x - 3x = 12 \times 5$

$12x = 60$

$x = \frac{60}{12}$

$x = 5$

With the value of $x$, we conclude that the first three terms are as follows:

First term $= 3x = 3×5 = 15$

Second term $= 3x - 6 = 15 - 6 = 9$

Third term $= \frac{3x}{5} =\frac{15}{5}= 3$