Question

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

Answer 1

The sequence given is:

2, 5, 11, 20, …

The general term for the n-th row of this arithmetic progression can be expressed as:

$T_n = \frac{3n^2 - 3n + 4}{2}$

For the 10th row, we substitute $n = 10$:

$T_{10} = \frac{3(100) - 3(10) + 4}{2} = \frac{300 - 30 + 4}{2} = \frac{274}{2} = 137$

Since there are 10 terms in the 10th row, with a common difference $c.d. = 3$, the sum of the terms of the 10th row is given by:

$\text{Sum} = \frac{10}{2} (2 \times 137 + 9 \times 3)$

Calculating:

$\text{Sum} = 5 (274 + 27) = 5 \times 301 = 1505$

Answer: 1505