Question

(1.3) Sequence A: 4; 7; 10; 13; 16; Sequence B: 5; 10; 20; 40; 80; .......... Sequence C: 2; 5; 10; 17; 26; (1.3.1) Write down the next three numbers in each of given sequences. (3) Sequence A Sequence B: Sequence C: (1.3.2) Write down how you decided what the next number would be in each of the three sequences. (3) Sequence A: Sequence B: Sequence C ​

Answer 1

Answer with Step-by -step explanation:

Sequence A;4,7,10,13,16

$a_2-a_1=7-4=3$

$a_3-a_2=10-7=3$

The difference between two consecutive terms is equal. Therefore, it forms arithmetic sequence.

Common difference, d=3

a=4

$a_n=a+(n-1)d$

$a_6=a+5d=4+5\times 3=19$

$a_7=a+6d=4+6(3)=22$

$a_8=a+7d=4+7(3)=25$

Sequence B: 5,10,20,40,80,...

$a_1=5,a_2=10,a_3=20$

$\frac{a_2}{a_1}=\frac{10}{2}=2$

$\frac{a_3}{a_2}=\frac{20}{10}=2$

The ratio  of two consecutive terms is equal. Therefore, it forms geometric sequence.

Common ratio, r=2

a=5

$a_n=a r^{n-1}$

$a_6=ar^5=5(2)^5=160$

$a_7=ar^6=5(2^6)=320$

$a_8=ar^7=5(2^7)=640$

Sequence C:2,5,10,17,26,..

a1=2

$a_2=5=2+3=a_1+3$

$a_3=10=5+5=a_2+5$

$a_4=17=10+7=a_3+7$

$a_5=26=17+9=a_4+9$

From the following pattern

We can get

$a_6=a_5+11=26+11=37$

$a_7=a_6+13=37+13=50$

$a_8=a_7+15=50+15=65$