Question

If 5 times the 5th term of an. AP is equal to 10 terms its 10th term, find the 15th term of the A.P

Answer 1

Correct question :

If 5 times the 5th term of an. AP is equal to 10 times its 10th term, find the 15th term of the A.P.

ANSWER -

Given :

• 5 times the 5th term = 10 times the 10th term

To find :

• 15th term

Formula used :

$\sf \bullet \: a_n\:=\:a \: + \: (n-1)d$

Here,

• aₙ = nth term
• a = 1st term
• d = common difference
• n = number of terms

Solution :

Let -

• a = 1st term of A.P.
• d = common difference of A.P.

Now let us find , 15th term firstly,

$\sf \implies \: a_{15}\:=\:a \: + \: (15-1)d$

$\sf \implies \: a_{15}\:=\:a \: + \: 14d \: \: \: \: \: equation \: 1$

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Now according to question,

➝ 5 × ( a₅ ) = 10 × ( a₁₀ )

Note -

• a₅ = a + (5-1)d
• a₁₀ = a + (10-1)d

➝ 5 × ( a + (5-1)d ) = 10 × ( a + (10-1)d )

➝ 5 × ( a + 4d ) = 10 × ( a + 9d )

➝ 5a + 20d = 10a + 90d

➝ 10a + 90d - ( 5a + 20d) = 0

➝ 10a + 90d - 5a - 20d = 0

➝ 10a - 5a + 90d - 20d = 0

➝ 5a + 70d = 0

➝ 5(a + 14d) = 0

➝ a + 14d = 0/5

➝ a + 14d = 0

[ Note- Form equation 1 we know that a + 14d = a₁₅ ]

Therefore,

➝ a + 14d = 0

➝ a₁₅ = 0

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ANSWER :

a₁₅ = 0