Math, asked by ashipra501, 9 months ago

If the qth term of an AP is zero, show that 29th term is twice its 19th term.​

Answers

Answered by dkchakrabarty01
0

Answer:

a9=a+(9-1)d=0,

Step-by-step explanation:

So a+8d=0, a=-8d a29=a+28d =20d a19=a+18d=10d So a29=a19×2

Answered by anindyaadhikari13
2

Correct Question:-

➡ If the 9th term of an A.P. is zero then prove that, 29th term is twice the 19th term.

Proof:-

Let us assume that,

➡ First term of the A.P. = a and,

➡ Common Difference = d

Now,

Nth term of an A.P. = a + (n -1)d

So,

9th term = a + (9 - 1)d

= a + 8d

Now, it's given that, 9th term of the A.P. is zero.

➡ a + 8d = 0 .....(i)

Now,

29th term = a + (29 - 1)d

= a + 28d

19th term = a + (19 - 1)d

= a + 18d

Now,

29th term - 2 × 19th term

= a + 28d - 2 × (a + 18d)

= a + 28d - 2a - 36d

= -a - 8d

= -1(a + 8d)

= -1 × 0

= 0

Hence,

29th term - 2 × 19th term = 0

➡ 29th term = 2 × 19th term. (Hence Proved)

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