What is the sum of the first 20 terms of the arithmetic progression 5, 8, 11, 14?

The sum of the first 20 terms of the arithmetic progression 5, 8, 11, 14 is 670.

According to the provided reference, the sum of the first 20 terms of the given arithmetic progression (AP) is 670. This AP has a first term (a) of 5 and a common difference (d) of 3 (8-5 = 3, 11-8 = 3, and so on).

To understand how this sum is calculated, it's helpful to consider the formula for the sum of an arithmetic series:

S_n = n/2 * [2a + (n-1)d]

Where:

• S_n is the sum of the first n terms
• n is the number of terms
• a is the first term
• d is the common difference

In our case, we have:

• n = 20
• a = 5
• d = 3

Applying the formula:

S₂₀ = 20/2 [2 5 + (20 - 1) 3]
S₂₀ = 10 [10 + 19 3]
S₂₀ = 10 [10 + 57]
S₂₀ = 10 * 67
S₂₀ = 670

Therefore, the sum of the first 20 terms of the arithmetic progression is indeed 670 as stated in the reference.