Answered

Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Paulo makes a sequence of numbers.

He chooses a starting number and then subtracts equal amounts each time.

The third number in his sequence is 45.
The tenth number is -32.

What is the first number in his sequence.
Show your method.

Sagot :

ZackFry
45 - -32 = 45 + 32 = 77.  
10 - 3 = 7.
77 /7 = 11. 
Paulo takes 11 away from each number. 

11 + 11 = 22. 
45 + 22 = 67. 
The first number was 67. 
olemakpadu
The sequence is an Arithmetic Progression.
T  =  a + (n-1)d.
Where a = first term.
           d = common difference.
           n =  Number of term

let the first number = a.

Sequence =  a,  a -d, a-2d, a-3d, ......

3rd =  a -2d = 45      .............(i)
10th  =  a -9d = -32  .............(ii)

 (i) minus (ii).

(a -2d) - (a -9d) = 45 - (-32)
a -2d -a +9d  = 77
-2d + 9d  = 77
7d  = 77.  Divide by 7.
d = 77/7 = 11.

Substitute d =11, in (i)
a-2d = 45.
a - 2(11) = 45
a -22 = 45.
a = 45 + 22 = 67,
Therefore first term = 67.

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.