The first difference of a sequence is 5, 8, 11, 14,... The sum of the first two terms of the original sequence is 23. Find the first three terms of the original sequence

The first three terms of the original sequence are 9, 14, and 22.

Step-by-step explanation:

From the question,

The first difference of the sequence is 5, 8, 11, 14,... That is,

Where is the first term of the original sequence

is the second term of the original sequence

is the third term of the original sequence etc.

Also, from the question, the sum of the first two terms of the original sequence is 23; that is,

Now, we can find and by solving the following equations simultaneously

.......... (1)

......... (2)

From equation (1)

Then,

.......... (3)

Substitute the value of into equation (2)

Then, becomes

Then,

Hence, the first term of the original sequence is 9

Now, substitute the value of into equation (3)

Then, become

∴

Hence, the second term of the original sequence is 14

The third term of the original sequence is given by

Then,

Hence, the third term of the original sequence is 22.

Hence, the first three terms of the original sequence are 9, 14, and 22.

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-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0