Question

If 6th times the 6th term of an A.P. is equal to the 9 times the 9th term, show that its 15th term is zero​

Answer 1

Given :

• 6th time × 6th term = 9th time × 9th term

To prove :

• $\sf \: a_{15} = 0$

Solution :

$\rightarrow \sf \: 6(a + (6 - 1)d = 9(a + 9 - 1)d \\ \\ \rightarrow6( \sf \: a + 5d) = 9(a + 8d) \\ \\ \rightarrow \sf \: 6a + 30d = 9a + 72d \\ \\ \rightarrow \sf \: 9a - 6a + 72d - 30d = 0 \\ \\ \sf \rightarrow3a + 42d = 0 \\ \\ \sf \rightarrow \: 3(a + 14d) = 0 \\ \\ \sf \rightarrow \: a + (15 - 1)d = 0 \\ \\ \sf \red{ \boxed{ \green{ \sf \ a_{15} = a + (15 - 1)d }}} \\ \sf∴ a_{15} = a + 14d = 0$

☆ Hence Proved a₁₅ is equals to Zero.

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