Recursion Solving Online

Recursion is defined as the difference between the two terms in a sequence. Recursive formula is used to describe the first term of the sequence and also the next term in a sequence. For example, the sequence is 8, 13, 18, 23, 28, 33… Many websites concentrate on students learning subjects through online. In that learning through online about recursive formula is very easy to understand. Let us see about recursion solving online in this article.

Worked Examples to Recursion Solving Online

Example 1 to Recursion Solving Online:

If `a_n = 7n + 3` , than find the value of `a_5` .

Solution:

Step 1:

Given sequence is `a_n = 7n + 3.`

Step 2:

Finding the fifth term of the sequence

Here, `n = 5` and substitute in the sequence, we get,

`a_5 = 7(5) + 3`

`a_5 = 35 + 3`

Step 3:

By adding the above value, we get,

`a_5 = 38`

Step 4:

Therefore, the value of `a_5` in the given sequence is 38.

Example 2 to Recursion Solving Online:

Find the value of n, if `a_n = n^(3)` and `a_n = 27` .

Solution:

Step 1:

Given

Sequence is `a_n = n^(3)`

`a_n = 27`

Step 2:

Substitute the value of `a_n` in the given sequence, we get,

`27 = n^ (3)`

Step 3:

Taking cube values on both sides, we get,

`3^ (3) = n^ (3)`

Therefore, the n value for the given sequence is `n = 3` .

Example 3 to Recursion Solving Online:

If `a_1 = - 3` and `a_(n-1) = a_n + 5` . Find first three terms of the sequence.

Solution:

Step 1:

Given

Sequence is `a_(n-1) = a_n + 5`

`a_1 = - 3`

Step 2:

Change the sequence in the form of `a_n` , we get,

`a_n = a_(n-1) - 5`

Step 3:

Substitute the value of `a_1 = -3` in the sequence we find the second term,

`a_2 = a_1 - 5`

`a_2 = -3 - 5`

`a_2 = - 8`

Step 4:

Substitute the value of a_2 in the sequence we get the third term,

`a_3 = a_(2) - 5`

`a_3 = -8 - 5`

`a_3 = - 13`

Step 5:

Therefore, the first three terms in the given sequence are -3, -8, and -11.

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Practice Problems to Recursion Solving Online

Problem 1:

If `a_n = 8n + 9` , than find the value of `a_7` .

Solution: `a_7 = 65`

Problem 2:

Write the first three terms of the sequence `a_1 = -9` and the recursive formula is `a_(n-1) = a_n + 25` .

Solution: First three terms are -9, -34, and - 59