Statement 1 If a, b, c are in AP then (b-a)^2=(c-a)^2 and Statement 2 If a, b, c are in AP then

step 1 If we work on, statement one we have, so statement one says that ABC is an AP, B negative a whol

Statement 1 If a, b, c are in AP then (b-a)^2=(c-a)^2 and...

Statement 1 If $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in $\mathrm{AP}$ then $(\mathrm{b}-\mathrm{a})^{2}=(\mathrm{c}-\mathrm{a})^{2}$ and Statement 2 If $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in $\mathrm{AP}$ then $4\left(\mathrm{~b}^{2}-\mathrm{ac}\right)=(\mathrm{c}-\mathrm{a})^{2}$

Statement 1 If $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in $\mathrm{AP}$ then $(\mathrm{b}-\mathrm{a})^{2}=(\mathrm{c}-\mathrm{a})^{2}$
and
Statement 2 If $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in $\mathrm{AP}$ then $4\left(\mathrm{~b}^{2}-\mathrm{ac}\right)=(\mathrm{c}-\mathrm{a})^{2}$

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Key Concepts

Arithmetic Progression

An arithmetic progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant. This constant difference allows us to express the terms in a general form and derive relationships between any of the terms using algebraic methods.

Common Difference

The constant difference between consecutive terms in an arithmetic progression is known as the common difference. It is a fundamental concept used to express the relationship between the terms, such as by writing the middle term as the average of the first and last terms and establishing other relations involving differences and sums.

Algebraic Manipulation and Identity Verification

Algebraic manipulation is the process of rearranging and simplifying expressions to reveal hidden relationships or verify identities. In the context of arithmetic progressions, these techniques are used to derive and verify formulas that relate the differences and products of the sequence terms, which is essential for confirming or refuting proposed identities.

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