The sum of the first 10 terms of an arithmetic progression is 120 and the sum of first twenty is 840. find sum of first 30 terms

The sum of first 30 terms of the arithmetic progression is 2160.

Explanation:

For an arithmetic progression, the sum of first terms with first term as and common difference is given as:

Now, it is given that:

Now, plug in these values and frame two equations in

Now, we solve equations (1) and (2) for . Subtract equation (1) from equation (2). This gives,

Now, plug in the value of in equation (1) and solve for .

Plug in the values of in the sum formula to find the sum of first 30 terms.

Now, the sum of first 30 terms is given as:

Therefore, the sum of first 30 terms of the arithmetic progression is 2160.

the temperature of the gas, in k, not celsius.