Given:
a = first term
n = number of terms
d = commom difference
For an arithmetic sequence, the sum (S) of the terms is:

To solve this question, you have to find "n". To do it, follow the steps.
Step 1: Find "a" and "d"
a is the first term of the sequence, that is, a = 3.
d is the common difference and can be found by subtracting two consecutive numbers. d = 7 - 3; d = 4.
Step 2: Substitute the values in the equation.

Knowing that the sum is 1953:

Multiplying both sides by 2:

Step 3: Use the Baskara formula to find n.
For a quadratic equation ax2 + bx + c = 0, the roots x are:

So, the equation:

Can be written as:

And, substituting it in the Bhaskara formula:
![\begin{gathered} n=\frac{-2\pm\sqrt[]{2^2-4\cdot4\cdot(-3906)}}{2\cdot4} \\ n=\frac{-2\pm\sqrt[]{^{}4+62496}}{8} \\ n=\frac{-2\pm\sqrt[]{^{}62500}}{8} \\ n=(-2\pm250)/(8) \\ n_1=(-2+250)/(8)=(248)/(8)=31 \\ n_2=(-2-250)/(8)=(-252)/(8)=-31.5 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/8weabx95y470xwh6e4v2vuom8557b0hrsd.png)
Since the number of terms is a positive number, n = 31.
Answer:
There are 31 terms.