Question

What is the recursive definition, common difference. And next 3 terms for the arithmetic sequence .8, 1.6, 2.4, 3.2, 4,.....

Answer 1

Answer: The common difference is 0.8 and the next 3 terms are 4.8, 5.6, 6.4.

Step-by-step explanation:

The given arithmetic sequence is,

`0.8,1.6,2.4,3.2,4,...`

Since it is a arithmetic sequence, therefore the common difference is,

`d=a_2-a_1=1.6-0.8=0.8`

The recursive is the process in which the preceding term is used to find the next one.

The recursive formula of arithmetic sequence is,

`A(n)=a+(n-1)d`

Where, a is first term and d is common difference.

Since, the first term is 0.8 and common difference is 0.8.

`A(n)=0.8+(n-1)0.8`

We have to find next 3 terms, so we have to add 0.8 in preceding term of the sequence because the common difference is 0.8. The last given term is 4, So, first next term is,

`4+0.8=4.8`

Now the preceding term is 4.8, so the next term is,

`4.8+0.8=5.6`

Now the preceding term is 5.6, so the next term is,

`5.6+0.8=6.4`

Therefore the common difference is 0.8 and the next 3 terms are 4.8, 5.6, 6.4.