Question

if 8 times the 8 term of ap is equal to 12 times the 12 term show that 20 term is zero​

Answer 1

Step-by-step explanation:

8( 8th term) = 12( 12th term)

= 8( a+7d) = 12 ( a+11d)

= 2(a+7d) = 3(a+11d)

= 2a+14d= 3a+33d

= a= -19d

20th term = a+19d

= -19d+19d ( as a=-19d)

=0

Answer 2

$\LARGE{ \underline{\underline{ \sf{Required \: answer:}}}}$

GiveN:

• 8 times the 8 term of ap is equal to 12 times the 12 term.

To Prove:

• 20th term is 0?

Step-wise-Step Explanation:

We know that, nth term of an AP series is:

$\large{ \boxed{ \sf{Tn = a + (n - 1) d}}}$

where Tn = nth term and a = first term.

Using this,

• a8 = a + 7d
• a12 = a + 11d

According to question,

⇒ 8(8th term) = 12(12th term)

⇒ 8(a + 7d) = 12(a + 11d)

⇒ 8a + 56d = 12a + 132d

⇒ 12a + 132d - 8a - 56d = 0

⇒ 4a + 76d = 0

⇒ a + 19d = 0

⇒ a = -19d

We need to show: a20 = 0

= a20

= a + 19d

Putting the value of 'a'

= -19d + 19d

= 0

Hence, proved !!