Question

Write a recursive formula for the sequence 6,10,14,18,22,.The find the next term

Answer 1

Answer:

10

Step-by-step explanation:

Answer 2

A sequence can be represented explicitly or by recursions.

The recursive formula is: $\mathbf{T_n = T_{n-1} + 4}$ and the next term is 26

The sequence is given as: 6,10,14,18,22

Notice that the difference between successive terms is 4.

So, the nth term is:

$\mathbf{T_n = T_{n-1} + 4}$

The next term is the 6th term.

So, we have:

$\mathbf{T_6 = T_{6-1} + 4}$

$\mathbf{T_6 = T_{5} + 4}$

The 5th term is 22.

So, the equation becomes

$\mathbf{T_6 =22 + 4}$

$\mathbf{T_6 =26}$

Hence, the recursive formula is: $\mathbf{T_n = T_{n-1} + 4}$ and the next term is 26

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