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If 9th term of an A.P. is Zero, prove that its 29th term is double the 19th term.
If 9th term of an A.P. is Zero, prove that its 29th term is double the 19th term.
Arithmetic Progressions | CBSE | Class 11 | Exercise 19.2 | Maths | RD Sharma
If 9th term of an A.P. is Zero, prove that its 29th term is double the 19th term.

Answer:

Given,

9th term of an A.P is 0

a9 = 0

an = a + (n – 1) d [w

When n = 9,

a9 = a + (9 – 1)d

= a + 8d

 

a9 = 0

a + 8d = 0

a = -8d

When n = 19,

a19 = a + (19 – 1)d

= a + 18d

= -8d + 18d

= 10d

When n = 29,

a29 = a + (29 – 1)d

= a + 28d

= -8d + 28d [Since, a = -8d]

= 20d

= 2×10d

a29 = 2a19

Thus, Proved.

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