Question

if the 9th term of AP is zero prove that its 29th term is twice its 19th term

Answer 1

If 9th term of An AP is 0,

A9 = a + (9 - 1 ) d

0 = a + 8d

a = - 8d

29th term, A29 = a + 28 d

A29 = - 8d + 28 d = 20d

19 th term, A19 = a + 18 d

A19 = - 8d + 18d = 10 d

A29 / A 19 = 20d / 10 d

A29 / A19 = 2 / 1

A29 = 2 * A 19.

Hence, PROVED.

Answer 2

Answer:

Step-by-step explanation:

a9=0

a1+8d=0

a1=-8d

for a29

a29=a1+28d

put a1= -8d in above equation

a29=28d-8d

a29=20d          ................................eq1

for a19

a19=a1+18d

put a1=-8d

a19=18d-8d

a19=10d                ..........................eq 2

from eq 1 and 2 we can conclude that

a29=2(10d)

a29=2(a19)

hence proved

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