Question

7. If 9th term of an A.P. is zero, prove that its 29th term is double (twice) the 19th term.

Answer 1

AP ( Arithmetic progression).
An arithmetic progression is a list of numbers a1, a2, a3 ………….. an in which each term is obtained by adding a fixed number to the preceding term except the first term.
This fixed number is called the common difference( d ) of the AP. Common difference of an AP will be the difference between any two consecutive terms.

a2= a1+d
a3= a2+d
a4= a3+d
……..
an= an-1+d ………

Each of the numbers in the list is called a term .

Method to find the common difference :
d = a2 - a1 or a3 - a2 or a4 - a3...

General form of an AP.:
a, a+d, a+2d, a+3d…….

Here a is the first term and d is common difference.

General term or nth term of A.P
The general term or nth term of A.P is given by an = a + (n – 1)d, where a is the first term, d is the common difference and n is the number of term.

SOLUTION IS IN THE ATTACHMENT..

HOPE THIS WILL HELP YOU….

Answer 2

Let a , d are first term and common

difference of an A.P.

i ) It is given that ,

9th term = 0

=> a + 8d = 0

a = -8d ---( 1 )

ii ) 19th term = a19

a19 = a + 18d

=> a19 = -8d + 18d

= 10d ---( 2 )

iii ) 29 the term = a29

= a + 28d

= - 8d + 28d

= 20d

= 2 × 10d

= 2 × a19 [ from ( 2 ) ]

Therefore ,

a29 = 2 × a19

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