Solve what of the others You only did 1-3

Question

ScanSolve AI Tutor · Accepted Answer

Okay, I understand. You're referring to the sequence questions from the first image you sent. I've solved the first two. Let's do the next one.

Analyze the given sequence to find the pattern.
The sequence is: $1, 3, 6, 10, x, 21, 28$ .
Let's look at the differences between consecutive terms:
$3 - 1 = 2$
$6 - 3 = 3$
$10 - 6 = 4$
Identify the pattern in the differences.
The differences are increasing by 1 each time: $2, 3, 4, \dots$
So, the next difference should be 5.
Apply the pattern to find the value of $x$ .
To find $x$ , we add the next difference (5) to the last known term (10):
$x = 10 + 5$ $x = 15$
Verify the pattern with the subsequent terms.
If $x = 15$ , the next difference should be 6:
$21 - 15 = 6$ (This matches the pattern)
The next difference should be 7:
$28 - 21 = 7$ (This also matches the pattern)

The value of $x$ is $\boxed{15}$ .

Answer