Question

The sequence shown: 28, 22, 16, 10...)

Answer 1

Recursive formula: $a_n = a_{n-1} -6$

Explicit Formula: $a_n = 34-6n$

35th term: -176

Sum of first 35 terms: -2590

Step-by-step explanation:

Given sequence is:

28, 22, 16, 10

First of all, we have to determine if this is an arithmetic sequence or geometric sequence. for this purpose we will find the common difference.

Here

$a_1 = 28\\a_2 = 22\\a_3 = 16$

$d = a_2-a_1 = 22-28 =-6\\d = a_3-a_2 = 16-22 = -6$

As the common difference is same the sequence is an arithmetic sequence

Recursive Formula:

Recursive formula is the formula that uses the previous term and common difference to find the next term

As the common difference is -6

The recursive formula will be:

$a_n = a_{n-1} +(-6)\\a_n = a_{n-1} -6$

Explicit formula:

The explicit formula for an arithmetic sequence is:

$a_n = a_1+(n-1)d$

Putting the value of d and a_1

$a_n = 28 + (n-1)(-6)\\= 28 -6n+6\\= 34-6n$

35th term of the sequence:

To find the 35th term, putting n = 35

$a_{35} = 34-6(35)\\a_{35} = 34 - 210\\a_{35} = -176$

Sum:

$a_1 = 28\\a_{35} = -176$

The formula for sum of finite arithmetic sequence is:

$S_n = \frac{n}{2} (a_1+a_n)$

As we have to find sum of 35 terms, the formula will be:

$S_{35} = \frac{35}{2}(28-176)\\S_{35} = 17.5 (-148)\\=-2590$

Hence,

Recursive formula: $a_n = a_{n-1} -6$

Explicit Formula: $a_n = 34-6n$

35th term: -176

Sum of first 35 terms: -2590

Keywords: Arithmetic sequence, common difference

Learn more about arithmetic sequence at:

• brainly.com/question/10941043
• brainly.com/question/10978510

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