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.

50

step-by-step explanation:

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500