Here is an identity.

Express the terms of the following sequence by giving a recursive formula.

emmasim [6.3K]

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

$a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\$

Step-by-step explanation:

First of all, we have to determine if the given sequence is arithmetic sequence or geometric. For that purpose, we calculate the common difference and common ratio

Given sequence is:

11,4,-3,-10,-17...

Here

$a_1 = 11\\a_2 = 4\\a_3 = -3\\So,\\d = a_2 - a_1 = 4-11 = -7\\d = a_3-a_2 = -3-4 = -7$

As the common difference is same, given sequence is an arithmetic sequence.

A recursive formula is a formula that is used to generate the next term of the sequence using the previous term and common difference

So, the recursive formula for an arithmetic sequence is given by:

$a_n = a_{n-1} +d\\Putting\ d = -7\\a_n = a_{n-1}-7$

Hence,

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

$a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\$

Keywords: arithmetic sequence, common difference

Learn more about arithmetic sequence at:

#LearnwithBrainly

6 0

3 years ago

HELP AND EXPLAIN PLSS

balu736 [363]

Answer:

Amount they ate is 6/8 or 3/4 of the pizza

Amount left over is 2/8 or 1/4 of the pizza.

Step-by-step explanation:

your family at 6 out of 8 pieces and simplified thats 3/4 if you divide both by 2

so the pieces left over would be 2 pieces or 2 out of the 8 pieces are left over.

making your fraction 2/8

Now you simplify and you can divided both 2 and 8 by 2

Making your other fraction 1/4

8 0

2 years ago

In Maria's physics class, she had to solve the equation 5=12at2+ut+x for u.

olasank [31]

Answer:

u= 5/t-12at-x/t

Step-by-step explanation:

I dont know what youre asking but that is the solved equation

7 0

2 years ago

What is two and one-fourth subtracted by one-eighth?

Illusion [34]

Two and one eighth is the answer

3 0

2 years ago

Sum of two numbers is 84. If one of the numbers exceeds the other by 12, the numbers are

djverab [1.8K]

Answer:

54 and 30

Step-by-step explanation:

84÷2=42-12=30

42+12=54

5 0

3 years ago