Question

What will come in place of the question mark (?) in the following series ?
148,197,233,258,274?

Answer 1

in between them there is a difference

so the difference is going on decreasing

so the next numbers is 280

Answer 2

Step-by-step explanation:

Given:

$148,197,233,258,274,?$

To find:

The next number in the sequence $148,197,233,258,274,?$

Solution:

$148,197,233,258,274,...$

Here the starting number is $148$ and the next number is $197$. We can start our answer from this.

Here subtract $197$ by $148.$

⇒ $197-148=49$

Here the number $49$ can be represented as $7^{2}.$

Now subtract the next number $233$ by $197.$

⇒ $233-197=36$

The number $36$ can be represented as $6^{2}$.

Now subtract the next number $258$ by $233.$

⇒ $258-233=25$

Here the number $25$ can be represented as $5^{2}$.

Now subtract the next number $274$ by $258$.

⇒ $274-258=16$

Here are the differences between the two numbers $16$ that be represented as $4^{2}.$

From the above, we can see that the differences between the numbers are reduced $7^{2} ,6^{2} ,5^{2}, 4^{2}$ in the square form.

So the next difference between the two numbers is $9$ and it can be represented as $3^{2}.$

Therefore subtract $283$ by $274$ and we get $9.$

⇒ $283-274=9$

So the next number in the series is $283.$

∴ The series is,

$148,197,233,258,274,283.$

Answer:

Hence the next number in the series $148,197,233,258,274$ is $283.$