Add three numbers up to two digits each

Learning Objectives Represent three two-digit numbers as terms in an arithmetic sequence using algebraic notation. Derive and apply a formula for the sum of three consecutive terms in an arithmetic sequence. Analyze the algebraic properties of the sum of three terms, such as its relationship to the middle term and its divisibility. Solve problems where the sum is given and one or more terms are unknown. Verify if three given two-digit numbers can be consecutive terms of an arithmetic sequence. Connect the arithmetic process of adding three numbers to the algebraic concept of a series sum. Use the sum of three terms to calculate their arithmetic mean efficiently. You can add 41 + 44 + 47 in your head instantly, but can you prove algebraically why the sum is always a multipl...

TermDefinitionExample Arithmetic SequenceA sequence of numbers in which the difference between any two consecutive terms is constant. This constant difference is called the common difference (d).The sequence 12, 19, 26, 33... is an arithmetic sequence with a first term (a₁) of 12 and a common difference (d) of 7. TermAn individual number in a sequence. The nth term is denoted by a_n.In the sequence 12, 19, 26, 33..., the third term (a₃) is 26. Consecutive TermsTerms that follow each other directly in a sequence.In the sequence 12, 19, 26, 33..., the numbers 19, 26, and 33 are three consecutive terms. Algebraic Representation of Consecutive TermsUsing variables to express consecutive terms in an arithmetic sequence to analyze their properties.Three consecutive terms can be represented as a...

Sum of Three Consecutive Terms (General Form) S_3 = a_n + a_{n+1} + a_{n+2} This is the fundamental definition. To analyze it algebraically, we substitute the general term formula a_n = a_1 + (n-1)d into it. Sum of Three Consecutive Terms (Simplified Formula) S_3 = 3 \cdot a_{n+1} The sum of three consecutive terms in an arithmetic sequence is always three times the middle term. This is a powerful shortcut for calculation and analysis. It's derived from S₃ = (a_{n+1} - d) + a_{n+1} + (a_{n+1} + d) = 3a_{n+1}. Finding the Middle Term from the Sum a_{n+1} = \frac{S_3}{3} If you know the sum of three consecutive terms, you can find the middle term by dividing the sum by 3. This also proves that the sum must be divisible by 3.