Question

If the numbers m - 2, 4m - 2 and 5m + 2
are in AP, find the value of 'm'.​

Answer 1

Step-by-step explanation:

we know that

if any sequence is in AP

then, t2-t1=t3-t2

(4m-2) - (m-2)= (5m+2) - (4m-2)

4m-2-m+2=5m+2-4m+2

3m=m+4

2m=4

m=2 answer

Answer 2

The value of m is 2.

• A term which is called common difference is used in the case of arithmetic progressions and sequences. One example of sequence in real life is the commemoration of birthdays of individuals. In this instance, there is typically a one-year gap between consecutive celebrations of the same person.
• The difference between any term and its preceding term is an arithmetic sequence's is referred to as the common difference. An arithmetic sequence always adds (or subtracts) the same amount to go from one term to the next.
• The amount that is added (or removed) at each point in an arithmetic progression is referred to as the "common difference" because, if we subtract (that is, if we determine the difference of) succeeding terms, we will always arrive at this common value.

Here, we are given that,

The numbers m - 2, 4m - 2 and 5m + 2 are in AP.

This means that the difference between the terms that is the common difference must be the same.

Then, we get,

$4m-2-m+2= 5m+2-4m+2.$

Or, $3m= m+4.$

Or, $2m = 4.$

Or, m = 2.

Hence, the value of m is 2.

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