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Determine 'a' so that 2a+1,{ a }^{ 2 }+a+1 and { 3a }^{ 2 }-3a

Question

Determine 'a' so that $2 a + 1, a^{2} + a + 1$ and $3 a^{2} - 3 a + 3$ are consecutive terms of an A .P.

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Determine 'a' so that

2 a + 1, a^{2} + a + 1

and

3 a^{2} - 3 a + 3

are consecutive terms of an A .P.

5 mins ago

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5 mins ago

Text solutionVerified

If a, b, c are in AP then

2 b = a + c

So,

2 (a^{2} + a + 1) = 3 a^{2} - 3 a + 3 + 2 a + 1

2 a^{2} + 2 a + 2 = 3 a^{2} - a + 4

\Rightarrow 3 a^{2} - 2 a^{2} - a - 2 + 4 - 2 = 0

\Rightarrow a^{2} - 3 a + 2 = 0

\Rightarrow a^{2} - 2 a - a + 2 = 0

\Rightarrow a (a - 2) - 1 (a - 2) = 0

(a - 1) (a - 2) = 0

a = 1

a = 2

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Question Text	Determine 'a' so that $2 a + 1, a^{2} + a + 1$ and $3 a^{2} - 3 a + 3$ are consecutive terms of an A .P.
Answer Type	Text solution:1
Upvotes	150