Question

if 5 times the 5th term of an AP is equal to 10 times its 10th term , find the 15th term of the AP​

Answer 1

Answer :

15th term of the AP = 0

Step-by-step explanation :

Given,

• 5 times the 5th term of an AP is equal to 10 times its 10th term

To find,

• 15th term of the AP

Solution,

  we know,

nth term of an AP is given by,

  $\boxed{\bf a_n=a+(n-1)d}$

where

a - first term

d - common difference

5th term :

a₅ = a + (5 - 1)d

a₅ = a + 4d

10th term :

a₁₀ = a + (10 - 1)d

a₁₀ = a + 9d

According to the question,

5 × a₅ = 10 × a₁₀

5 ( a + 4d ) = 10 ( a + 9d )

5a + 20d = 10a + 90d

10a - 5a = 20d - 90d

5a = -70d

a = -70d/5

a = -14d

a + 14d = 0

we have to find the 15th term

a₁₅ = a + ( 15 - 1 )d

a₁₅ = a + 14d

a₁₅ = 0

∴ 15th term of the AP = 0

Answer 2

15th term of the AP = 0

Step-by-step explanation :

Given,

• 5 times the 5th term of an AP is equal to 10 times its 10th term

To find,

• 15th term of the AP

Solution,

we know,

nth term of an AP is given by,

$\boxed{\bf a_n=a+(n-1)d}$

where

• a - first term

• d - common difference

5th term :

a₅ = a + (5 - 1)d

a₅ = a + 4d

10th term :

a₁₀ = a + (10 - 1)d

a₁₀ = a + 9d

According to the question,

5 × a₅ = 10 × a₁₀

5 ( a + 4d ) = 10 ( a + 9d )

5a + 20d = 10a + 90d

10a - 5a = 20d - 90d

5a = -70d

a = -70d/5

a = -14d

a + 14d = 0

we have to find the 15th term

a₁₅ = a + ( 15 - 1 )d

a₁₅ = a + 14d

a₁₅ = 0

∴ 15th term of the AP = 0