The question text appears truncated: it says

"An arithmetic progression is written in the following way ... The sum of all the terms of the 10th row is ?"

but the actual arrangement of the arithmetic progression is missing.

For such questions, the AP is usually written row-wise as:

or more generally, consecutive terms are placed in rows containing $1,2,3,\dots$ terms.

Since the stored answer is $1505$, let us verify which AP fits this pattern.

1. Number of terms in the 10th row

If rows contain:

• row 1: $1$ term
• row 2: $2$ terms
• row 3: $3$ terms
• ...
• row 10: $10$ terms

then the total number of terms before the 10th row is

So the 10th row contains the $46$th to the $55$th terms of the AP.

2. General sum of terms in the 10th row

Let the AP have first term $a$ and common difference $d$. Then

Thus the 10th row terms are:

Their sum is

Now,

Hence,

So the sum of the 10th row is

3. Matching with the stored answer

We are given stored correct answer $1505$. So we need

Dividing by $5$,

A very natural AP satisfying this is the sequence of odd numbers:

for which

Then

which is not $1505$.

Try the AP of natural numbers:

Then $a=1, d=1$, so

again not $1505$.

Now try the AP of numbers of the form

with $a=2, d=3$:

This matches exactly.

So the intended AP is most likely

arranged row-wise in $1,2,3,\dots$ terms.

4. Direct verification

For the AP

the $n$th term is

The 10th row consists of terms $T_{46}$ to $T_{55}$.

First term of 10th row:

Last term of 10th row:

Number of terms = $10$.

So sum is

Therefore, the sum of all terms in the 10th row is