If you start with 1 push-up, then do 2 the next time, then 3, then 4, and keep adding one more push-up each session, the question is not just how many push-ups you do in one workout. The real question is how many sessions it takes for your total number of push-ups to reach 150.

This creates a growing pattern:

1
1 + 2 = 3
1 + 2 + 3 = 6
1 + 2 + 3 + 4 = 10

Each time, the total builds on everything that came before. This kind of pattern is called a triangular number pattern, because the totals come from adding counting numbers in order.

To find the total after a certain number of sessions, you use this formula:

total = n(n + 1) / 2

Here, n means the number of times you have done your push-ups.

So to reach 150, set the formula equal to 150:

n(n + 1) / 2 = 150

Multiply both sides by 2:

n(n + 1) = 300

Now test nearby whole numbers:

16 × 17 = 272
17 × 18 = 306

Since 300 falls between those two, 16 sessions is not enough, but 17 sessions is enough.

Now check the totals:

After 16 sessions:
16 × 17 / 2 = 136

After 17 sessions:
17 × 18 / 2 = 153

That means you will reach at least 150 total push-ups on your 17th time.

So the answer is 17 times.

By the end of the 17th session, you will have done 153 push-ups in total. That is 3 more than 150. If you stop after 16 sessions, you will only have done 136 total push-ups, which is 14 short.

This is a good example of how small increases add up faster than they seem. Even though each session only increases by 1 push-up, the running total grows steadily and reaches 150 sooner than many people expect.