Question

If 6times the 6th term of an ap is equal to the 14times the 14th term, show that 20th term is 0...

Answer 1

Step-by-step explanation:

6th term of AP is = a + 5d

14th term of AP is = a + 13d

20th term of AP is = a + 19d

given that 6 times 6th term = 14 times 14th term

$6(a + 5d) = 14(a + 13d) \\ 6a + 30d = 14a + 182d \\ 14a + 182d - 6a - 30d = 0 \\ 8a + 152d = 0 \\ 8(a + 19d) = 0 \\ a + 19d = \frac{0}{8} \\ a + 19d = 0$

hence proved

hope you get your answer

Answer 2

Concept:

If $a$ is the first term of an Arithmetic progression (AP) and the common difference is d then the n-th term or the general term formula for that Arithmetic Progression is given by,

$a_n=a+(n-1)d$

Given:

Given that the 6 times of 6th term of an AP is equal to the 14 times of 14th term.

Find:

The 20 th term of that AP.

Solution:

Let the first term be a and the common difference of the progression be d.

6th term = a+(6-1)d = a+5d

14 th term =a+(14-1)d = a+13d

According to question,

6(a + 5d) = 14(a + 13d)

6a + 30d = 14a + 182d

14a - 6a = 30d - 182d

8a = -152d

a = -152d/8 = -19d

Now, the 20th term of the AP is = a + (20-1)d= a + 19d = -19d + 19d = 0

Hence it is proved that 20th term of AP is 0.

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