103k views
5 votes
DOES ANYONE KNOS THE ANSWER

DOES ANYONE KNOS THE ANSWER-example-1

1 Answer

6 votes

Answer:

Explanation:

Let's find the first six terms of the original sequence for each of the given cases:

a. The first term of the original sequence is 3:

In this case, we can start with the first term as 3 and use the differences provided to find the subsequent terms:

1st term: 3 (given)

2nd term: 3 + 2 = 5

3rd term: 5 + 5 = 10

4th term: 10 + 8 = 18

5th term: 18 + 11 = 29

6th term: 29 + 14 = 43

So, the first six terms of the original sequence are 3, 5, 10, 18, 29, and 43.

b. The sum of the first two terms in the original sequence is 12:

In this case, we know that the sum of the first two terms is 12. Let's call the first term "a" and the second term "b." So:

a + b = 12

We also have the differences:

2 (from a to b)

5 (from b to the next term)

8

11

14

Let's solve for a and b:

From the given differences:

a + 2 = b

b + 5 = (b + 2) + 5 = b + 7

(b + 2) + 8 = b + 10

(b + 10) + 11 = b + 21

(b + 21) + 14 = b + 35

Now, let's check when a + b = 12:

a + (a + 2) = 12

2a + 2 = 12

2a = 12 - 2

2a = 10

a = 5

Now that we have a = 5, we can find b:

a + 2 = b

5 + 2 = b

b = 7

So, the first two terms of the original sequence are 5 and 7. We can use these values to find the subsequent terms, as shown in part (a).

c. The fifth term in the original sequence is 34:

In this case, we need to find the first term "a" and then use the differences to find the fifth term. Let's call the first term "a":

a + 2 = 34 (since the fifth term is 34)

a = 34 - 2

a = 32

Now that we have a = 32, we can find the second term:

a + 2 = b

32 + 2 = b

b = 34

Now, using these values for a and b, we can find the subsequent terms as shown in part (a):

1st term: 32

2nd term: 34

3rd term: 34 + 2 = 36

4th term: 36 + 5 = 41

5th term: 41 + 8 = 49

6th term: 49 + 11 = 60

So, the first six terms of the original sequence are 32, 34, 36, 41, 49, and 60.

User MEric
by
8.1k points

Related questions

asked Oct 24, 2024 10.7k views
Trungnt asked Oct 24, 2024
by Trungnt
7.9k points
1 answer
2 votes
10.7k views
asked Mar 21, 2024 134k views
Timur Shtatland asked Mar 21, 2024
by Timur Shtatland
8.2k points
1 answer
0 votes
134k views