Question

someone help me. write two different sequences whose first three terms are 1,2, &4. Describe each pattern. i already have 1,2,4,8,16,32,... ( the number is two times the previous number) i just cant figure out any more and the ones i have thought of i got wrong

Answer 1

how about 1,2, 4, 7, 11, 16,...

Answer 2

i tried that answer but my teacher told me it was incorrect

Answer 3

`way 1`
\(1,~2,~4,~8,~16,~32\)
regular geometric sequence r=2 as you say.

`way 2`
\(1,~2,~4,~7,~11,~16\)
you add +1, +2, +3 and so on as satellite suggested.

`way 3`
\(1,~2,~4,~9,~23,~64\)

\(a_{2}=3a_{1}-1\quad \Longrightarrow \quad 3\cdot 1-1=2\)
\(a_{3}=3a_{2}-2\quad \Longrightarrow \quad 3\cdot 2-2=4\)
\(a_{4}=3a_{3}-3\quad \Longrightarrow \quad 3\cdot 4-3=9\)
\(a_{5}=3a_{4}-4\quad \Longrightarrow \quad 3\cdot 9-4=23\)
\(a_{6}=3a_{5}-5\quad \Longrightarrow \quad 3\cdot 23-5=64\)

this satisfies the formula,
\(a_{n+1}=3a_{n}-n\)

Answer 4

With only three numbers you can make almost any pattern...

Answer 5

thank you