What are the three terms in an A.P. with a sum of 36 and a product of 1428?

In summary, the conversation discusses solving for three consecutive terms of an arithmetic progression (A.P.) with a sum of 36 and a product of 1428. The first piece of information is that a1 * a2 * a3 = 1428, and the second piece of information is that a1 * (a1 + d) * (a1 + 2d) = 1428, where d is the difference between the terms. This leads to having 2 variables and 2 equations to solve for the three terms.
  • #1
tykescar
6
0
This isn't a homework question, it's in a textbook I have and I'm a bit stumped. I know there's something relatively simple I'm missing so any help would be much appreciated (working too).

Three consecutive terms of an A.P. have a sum of 36 and a product of 1428. Find the three terms.
 
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  • #2
alright so you have two pieces of information here.

you have the fact that a1 * a2 * a3 = 1428

and if d is the difference between a1-a2 and a2-a3,

then you have; a1* (a1 + d) * (a1 + 2d) = 1428

so that's the first piece of information. Do you think you could put the second piece of information in terms of a1 and d, and then you would have 2 variables and 2 equations.
 
  • #3
Brilliant. Thanks very much for your help.
 

FAQ: What are the three terms in an A.P. with a sum of 36 and a product of 1428?

What is an arithmetic progression?

An arithmetic progression, also known as an arithmetic sequence, is a sequence of numbers in which each term is obtained by adding a constant value to the previous term. The constant value is called the common difference, and it determines the pattern of the sequence.

What is the formula for finding the nth term in an arithmetic progression?

The formula for finding the nth term in an arithmetic progression is: an = a1 + (n-1)d, where an represents the nth term, a1 represents the first term, and d represents the common difference.

How can you determine if a sequence is an arithmetic progression?

To determine if a sequence is an arithmetic progression, you can check if the difference between consecutive terms is constant. If the difference is the same for every pair of terms, then the sequence is an arithmetic progression.

Can an arithmetic progression have a negative common difference?

Yes, an arithmetic progression can have a negative common difference. This means that the sequence is decreasing instead of increasing. For example, an arithmetic progression with a first term of 10 and a common difference of -3 would be: 10, 7, 4, 1, -2, ...

What are some real-life applications of arithmetic progressions?

Arithmetic progressions are commonly used in finance and economics to model linear growth or depreciation. They are also used in physics to describe the motion of an object with a constant acceleration. In computer science, arithmetic progressions are used in algorithms and data structures to perform sequential operations on a set of data.

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