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3 years ago

Pattern: 0, 1, 3, 6, 10, 15, __ Explain the pattern of these numbers.

Mathematics

1 answer:

chubhunter [2.5K]3 years ago

5 0

Answer:

Step-by-step explanation:

0 + 1 = 1

1 + 2 = 3

3 + 3 = 6

6 + 4 = 10

10 + 5 = 15

15 + 6 = 21

Each number is added to an increase of 1 - first add 1, then add 2, then add 3,etc

Not listed but next would be 21 + 7 = 28

so it would be 0, 1, 3, 6, 10, 15, 21, 28

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Solve linear equations -4(b+3)-12=2b-16+5b

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2 years ago

Given a term and the common difference, find the explicit formula. 8. a(19) = 135 d = 15

Rasek [7]

The explicit formula is a(n) = 15(n – 10)

Solution:

Given, a term a(19) = 135 and common difference d = 15

We have to find the explicit formula.

Now, we know that, a(n) = a + (n – 1)d where a(n) is nth term, a is first term, d is common difference,

So, for a(19)

$\begin{array}{l}{\rightarrow a(19)=a+(19-1) 15} \\\\ {\rightarrow 135=a+18 \times 15} \\\\ {\rightarrow a=135-270} \\\\ {\rightarrow a=-135}\end{array}$

Now, we know that, an explicit formula is an expression for finding the nth term,

So, in our problem, expression for finding nth term is a + (n – 1)d

$\begin{array}{l}{\rightarrow-135+(n-1) 15} \\\\ {\rightarrow-135+15 n-15} \\\\ {\rightarrow 15 n-150} \\\\ {\rightarrow 15(n-10)}\end{array}$

Hence, the explicit formula is a(n) = 15(n – 10).

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3 years ago