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CBSE Class 9 Mathematics Question 8 of 17

Proofs in Mathematics — Question 3

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Question 3

Let us look at the triangular numbers figure again. Add two consecutive triangular numbers. For example, T1 + T2 = 4, T2 + T3 = 9, T3 + T4 = 16.

What about T4 + T5 ? Make a conjecture about Tn-1 + Tn.

Let us look at the triangular numbers figure again. Add two consecutive triangular numbers. For example, T^1 + T^2 = 4, T^2 + T^3 = 9, T^3 + T^4 = 16. NCERT Class 9 Mathematics CBSE Solutions.
Answer

Given,

⇒ T1 + T2 = 4 = 22

⇒ T2 + T3 = 9 = 32

⇒ T3 + T4 = 16 = 42

Conjecture :

On adding two triangular numbers the resultant value is the square of the larger number.

By using conjecture :

⇒ T4 + T5 = 52 = 25.

Hence, Tn - 1 + Tn = n2.