Question

The first four terms of a sequence are shown below: 8, 5, 2, −1 Which of the following functions best defines this sequence?

Answer 1

Answer :

y = f(x) = 11 - 3x , x € N

Solution :

Here ,

The given sequence is : 8 , 5 , 2 , -1

Clearly ,

The given sequence is an AP , where

First term , a = 8

Common difference , d = 5 - 8 = -3

Also ,

The nth term of an AP is given by ;

a(n) = a + (n - 1)d .

Thus ,

The nth term of the given AP will be ;

=> a(n) = 8 + (n - 1)•(-3)

=> a(n) = 8 - 3n + 3

=> a(n) = 11 - 3n

Thus ,

The function representing the given sequence can be defined as :

y = f(x) = 11 - 3x , x € N .

Answer 2

$\huge{\boxed{\rm{Question}}}$

The first four terms of a sequence are shown below :

8, 5, 2, -1

Which of the following functions best defines this sequence ?

$\huge{\boxed{\rm{Answer}}}$

$\large{\boxed{\boxed{\sf{Given \: that}}}}$

• The first four terms of sequences are 8 , 5 , 2 , -1

$\large{\boxed{\boxed{\sf{To \: find}}}}$

• Which function's best defines this sequence.

$\large{\boxed{\boxed{\sf{Solution}}}}$

• y = f(x) = 11 - 3x , x€N is best defines this sequence.

$\large{\boxed{\boxed{\sf{What \: the \: question \: says}}}}$

$\large{\boxed{\boxed{\sf{Let's \: understand \: the\: concept \: 1st}}}}$

• This question says that there is a sequence given that is 8, 5, 2, −1. Afterwards it says that we have to find the the best defines function of this sequence

$\large{\boxed{\boxed{\sf{How \: to \: do \: this \: question}}}}$

$\large{\boxed{\boxed{\sf{Procedure \: of \: question \: is \: given \: below}}}}$

• Firstly, it's compulsory to know that this sequence is of A.P . And we know this then we also know this in given sequence the first term of AP is 8 and the common difference is 5 - 8 . Then we have to subtract them nd the result is -3. After that we know the 9th terms of the AP is given by the - a(n) = a + (n-1) d. Now we have to put the values according to this rule . After putting the values we get a result that is a(n) = 11 - 3n. ( Wow ) now it's cleared that what is our final result ‽ Our final result is f(x) = 11 - 3x , x€N. Hence, solved

$\large{\boxed{\boxed{\sf{Full \: solution}}}}$

We know that the given sequence is

8 , 5 , 2 , -1

From viewing this sequence we have cleared that this is an AP sequence !

$\small\purple{\texttt{Where the terms are}}$

• First term = 8.

• Common Difference = 5-8

☞ Common Difference = -3

We know that the 9th terms of the AP is given by the -

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

$\small\pink{\texttt{Substituting the values we get}}$

➜ a(n) = a + (n-1) d

➜ a(n) = 8 + (n-1) • (-3)

➜ a(n) = 8 - 3n + 3

➜ a(n) = 11 - 3n

Thus, we get our result.

Hence, the function best defines this sequence is y = f(x) = 11 - 3x , x€N

Answer = f(x) = 11 - 3x , x€N

Hope it's helpful

Thank you :)