Arithmetic Series Calculator

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Example

Created on 2024-06-20Asked by Luna Scott (Solvelet student)

Find the sum of the first 20 terms of the arithmetic series where the first term is 4 and the common difference is 3.

Solution

Step 1: Identify the first term (

a_1

) and the common difference (

d

). The first term is 4 and the common difference is 3. Step 2: Use the formula for the sum of the first

n

terms of an arithmetic series:

S_n = \frac{n}{2} (2a_1 + (n-1)d).

Step 3: Substitute

a_1 = 4

d = 3

, and

n = 20

into the formula:

S_{20} = \frac{20}{2} (2 \cdot 4 + (20-1) \cdot 3) = 10 (8 + 57) = 10 \cdot 65 = 650.

Step 4: Conclusion. The sum of the first 20 terms of the arithmetic series is 650. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Penelope Campbell on Solvelet

1. Find the first 100 positive integers sum 2. Find the average of the first 20 odd integers.,

DefinitionAn integer is the sum of the elements of an integer. The calculation formula is Sn ≤ = 1 2 n (a1 ≤ + an ≤); where Sn ≤ is the number of the first n elements, a1 ≤ is the first element, and a is the nth element. Arithmetic systems play an important role in calculating numbers and analyzing associated data, especially in various financial fields, computer algorithms and discrete mathematical concepts. For example: the arithmetic sequence 3,7,11,15, ¡ The first n terms can be calculated using the formula Sn ≤ = 1 2 n (3 + (3 + (n − 1) 4)).

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