What is the sum of the arithmetic sequence 3, 9, 15 if there are 26 terms?

The arithmetic sequence starts with the first term (a) as 3 and continues with a common difference (d) of 6 (since 9 – 3 = 6 and 15 – 9 = 6).

To find the sum of the first n terms of an arithmetic sequence, we can use the formula:

S_n = n/2 * (2a + (n – 1)d)

In this case, we have:

• a = 3 (first term)
• d = 6 (common difference)
• n = 26 (number of terms)

Now, plugging in these values into the formula:

S₂₆ = 26/2 * (2(3) + (26 – 1)(6))

This simplifies to:

S₂₆ = 13 * (6 + 150)

Continuing the calculation:

S₂₆ = 13 * 156

S₂₆ = 2028

So, the sum of the arithmetic sequence 3, 9, 15 with 26 terms is 2028.