Question

What is the term-to-term rule for the following sequences? Solve (A)A) 1,2,3,4,5,6,7,8,…B) 4,9,14,19,24,29,…C) 32,30,28,26,24,22,…D) 6,13,20,27,34,41,…E) 3,6,12,24,48,96,…F) 36,30,24,18,12,6,…G) -13,-11,-9,-7,-5,…H) 48,45,42,39,36,…I) 1,7,49,343,2401,…

Answer 1

A) Given:

The sequence is,

`1,2,3,4,5,6,7,8,…`

To find: The term-to-term rule

Since the given sequence has the common differnce 1.

So, it is of the arithmetic sequence.

Therefore, let us take

`a_1=1`

Then the second term will be,

`\begin{gathered} a_2=a_1+1 \\ =1+1 \\ =2 \end{gathered}`

The third term will be,

`\begin{gathered} a_3=a_2+1 \\ =2+1 \\ =3 \end{gathered}`

And so on.

So, the term to term rule must be,

`a_n=a_(n-1)+1`

Final answer: The term to term rule is,

`a_(n)=a_(n-1)+1`