Question

if the seventh term of an APis 1/9 and its ninth term is 1/7 ,find its(63)rd term

Answer 1

Answer:

The 63rd term of the AP is 1.

Step-by-step-explanation:

For an AP,

• t₇ = 1 / 9
• t₉ = 1 / 7

We have to find the 63rd term of AP.

We know that,

tₙ = a + ( n - 1 ) * d

⇒ t₇ = a + ( 7 - 1 ) * d

⇒ 1 / 9 = a + 6d

⇒ a = ( 1 / 9 ) - 6d

⇒ a = ( 1 - 54d ) / 9 - - - ( 1 )

Also,

t₉ = a + ( 9 - 1 ) * d

⇒ 1 / 7 = a + 8d

⇒ a + 8d = 1 / 7

⇒ [ ( 1 - 54d ) / 9 ] + 8d = 1 / 7 - - - [ From ( 1 ) ]

⇒ ( 1 - 54d + 72d ) / 9 = 1 / 7

⇒ 1 + 18d = 9 / 7

⇒ 18d = ( 9 / 7 ) - 1

⇒ 18d = ( 9 - 7 ) / 7

⇒ 18d = 2 / 7

⇒ d = 2 / 7 * 1 / 18

⇒ d = 1 / 7 * 1 / 9

⇒ d = 1 / 63

By substituting d = 1 / 63 in equation ( 1 ),

a = ( 1 - 54d ) / 9 - - - ( 1 )

⇒ a = [ 1 - 54 * ( 1 / 63 ) ] / 9

⇒ a = [ 1 - ( 6 / 7 ) ] / 9

⇒ a = [ ( 7 - 6 ) / 7 ] / 9

⇒ a = ( 1 / 7 ) / 9

⇒ a = ( 1 / 7 ) * ( 1 / 9 )

⇒ a = 1 / 63

Now,

t₆₃ = a + ( 63 - 1 ) * d

⇒ t₆₃ = ( 1 / 63 ) + 62 * ( 1 / 63 )

⇒ t₆₃ = ( 1 / 63 ) + ( 62 / 63 )

⇒ t₆₃ = ( 1 + 62 ) / 63

⇒ t₆₃ = 63 / 63

⇒ t₆₃ = 1

∴ The 63rd term of the AP is 1.