Answer to Question #299853 in Algebra for JEZ

Question

A. Write the missing term/s in the given series of numbers.

1. Find the next three terms in: 14, 10, 6, 2, ? , ? , ? .

2. Find the

th 35

term in the arithmetic sequence

3, 9, 15, 21, ? .

3. Find the next two terms in the sequence:

5, 2, 8, 3, 11, 4, 14, 5, 17, 6, ? , ? .

4. Find the next number:

2, 3, 4, 6, 6, 9, 8, ? .

5. What should become in place of x in the following series:

2, 2, 4, 12, 48, 240, x?

6. Identify the next number in the following series

2, 8, 26, 62, 122, 212, ? .

7. What is the next number in the pattern

4, 12, 36, 108, ? .

Answer 1

A.

1. $-14, -10, -6, -2, \textcolor{blue}{2,4,8},$

2. $a_1=3, d=9-3=6$

$$a_{35}=a_1+d(35-1)=3+6(35-1)=207$$

3.

Consider two sequences

$$5,8,11,14,17,20,23,...$$

$$2,3,4,5,6,7,8,...$$

Hence we have the sequence

$$5, 2,8, 3, 11, 4,14, 5,17,6, \textcolor{blue}{20,7},...$$

4.

Consider two sequences

$$2,4,6,8,10,...$$

$$3,6,9,12,...$$

Hence we have the sequence

$$2, 3,4,6, 6, 9, 8, \textcolor{blue}{12},...$$

5.

We see

$$2\cdot 1=2, 2\cdot 2=4, 4\cdot 3=12, 12\cdot 4=48,$$

$$48\cdot 5=240, 240\cdot 6=1440$$

Hence $x=1440$

6.

$$2\ \ \ \ \ \ \ 8\ \ \ \ \ \ \ 26\ \ \ \ \ \ \ 62\ \ \ \ \ \ \ 122\ \ \ \ \ \ \ 212\ \ \ \ \ \ \ \ 338\\$$

$$6\ \ \ \ \ \ \ \ 18\ \ \ \ \ \ \ \ 36\ \ \ \ \ \ \ \ 60 \ \ \ \ \ \ \ \ 90 \ \ \ \ \ \ \ \ 126\ \ \ \ \\$$

$$12\ \ \ \ \ \ \ \ 18 \ \ \ \ \ \ \ \ 24\ \ \ \ \ \ \ \ 30\ \ \ \ \ \ \ \ 36\ \ \ \ \ \\$$

$$6 \ \ \ \ \ \ \ \ \ \ 6\ \ \ \ \ \ \ \ \ \ 6\ \ \ \ \ \ \ \ \ \ 6\ \ \ \ \ \\ \\$$

Hence we have the sequence

$$2,8, 26, 62, 122, 212, \textcolor{blue}{338},...$$

7.

$$4\times 3=12, 12\times 3=36, 36\times 3=108,$$

$$108\times 3=324$$

Hence we have the sequence

$$4,12, 36, 108, \textcolor{blue}{324},...$$