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3 years ago

Es

Mathematics

1 answer:

Maru [420]3 years ago

4 0

C) They will remember their grandfather’s rhyme and always try their best.
Based on the fact that they didn’t want to interrupt their grandfather’s work shows that they care about him and the things he do so option A is out.
Option D is out also because there is no mention of their friends. (Based on the photo that is available along with the question.)
So all that is left is options B and C.
However, option B is out because if they were to write a book about their grandfather, how are they going to get information from just one rhyme he made?

So the answer is Option C.
(If I’m wrong, I’m sorry.)

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<h2>Answer:</h2>

Recursive equation for the pattern followed is given by,

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<h2>Step-by-step explanation:</h2>

In the question,

The number of interaction for 1 child = 0

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So,

We need to find out the pattern for the recursive equation for the given conditions.

So,

We see that,

$a_{1}=0\\a_{2}=1\\a_{3}=5\\a_{4}=14\\$

Therefore, on checking, we observe that,

$a_{n}=a_{n-1}+(n-1)^{2}$

On checking the equation at the given values of 'n' of, 1, 2, 3 and 4.

At,

n = 1

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{1}=a_{1-1}+(1-1)^{2}\\a_{1}=0+0=0\\a_{1}=0$

which is true.

At,

n = 2

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{2}=a_{2-1}+(2-1)^{2}\\a_{2}=a_{1}+1\\a_{2}=1$

Which is also true.

At,

n = 3

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{3}=a_{3-1}+(3-1)^{2}\\a_{3}=a_{2}+4\\a_{3}=5$

Which is true.

At,

n = 4

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{4}=a_{4-1}+(4-1)^{2}\\a_{4}=a_{3}+9\\a_{4}=14$

This is also true at the given value of 'n'.

Therefore, the recursive equation for the pattern followed is given by,

$a_{n}=a_{n-1}+(n-1)^{2}$

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