Step by step solution to "Please, continue the two sequences of numbers below..."

Sapewa

Answered question

2022-01-15

Please, continue the two sequences of numbers below and find an equation to each of the sequences:

n = 1, 2, 3, 4, 5, 6, 7

Equation

a_{n} = 2, 5, 9, 14, 20, 27

b_{n} = 1, 3, 12, 60, 360, 2520

Shannon Hodgkinson

Beginner2022-01-17Added 34 answers

You already have an answer for the first, so Ill

RizerMix

Expert2022-01-20Added 656 answers

First sequence:

a_{n} = 2, 5, 9, 14, 20, 27, . .

Thus,

a_{1} = 2

a_{2} = 5

a_{3} = 9

a_{4} = 14

Now,

a_{2} - a_{1} = 3

a_{3} - a_{2} = 4

a_{4} - a_{3} = 5

And so on..

a_{n} - a_{n - 1} = n + 1

This is cumulative sequence. Thus, we get

a_{n} - a_{1} = 3 + 4 + 5 + . . . + (n + 1)

\Rightarrow a_{n} - 2 = 3 + 4 + 5 + . . . + (n + 1)

\Rightarrow a_{n} = 2 + 3 + 4 + 5 + . . . + (n + 1)

\Rightarrow a_{n} = \frac{n}{2} [2 + (n + 1)]

Therefore,

a_{n} = \frac{n (n + 3)}{2}

Put

n = 7

a_{7} = \frac{7 (7 + 3)}{2} = \frac{7 \times 10}{2} = 35

Hence, the equation is

a_{n} = \frac{n (n + 3)}{2}

and

a_{7} = 35

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?