Question

What is the explicit formula for the sequence {3,8,13,18,…}?

A.) an=3+5(n−1)
B.) an=3−5(n−1)
C.) an=3+5n−1
D.) an=3+an−1

Answer 1

hey mate

here is your answer...

first term (a)=3

common difference (d)=5

thus,an=a+(n-1)d

=>3+(n-1)5

=>3+5(n-1)

thus, option A is correct.

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Answer 2

Answer:

So, option (a) $a_{n}= 3 + 5(n-1)$ is correct for the given sequence.

Step-by-step explanation:

Given sequence is {3,8,13,18,…}.

Given that each term has a common difference, this is an arithmetic sequence. In this instance, the next word in the sequence is obtained by adding 5 to the previous term.

So, in others word $a_{n} = a_{1} + d(n-1)$.

where $a_{1}$ = first term of sequence

           d = common difference

As we already know the formula of arithmetic sequence,

$a_{n}= a_{1} + d(n-1)$

So, substituting the values of $a_{1}$ = 3 and d = 5.

$a_{n}= 3 + 5(n-1)$

$a_{n}= 3 + 5n -5$

$a_{n} = 5n - 2$

Hence, according the given sequence  {3,8,13,18,…} the explicit formula is $a_{n}= 3 + 5(n-1)$.

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