Question

If 10 times of 10th term is equal to 20 times of 20th term of an A.P., find its 30th term.

Answer 1

Answer:

Step-by-step explanation:

let x be first term and a be the common difference 

10th term = x+9a

20th term=x+19a

30th term=x+29a

given

10*10th term=20*20th term

10(x+9a)=20(x+19a)

10x+90a=20x+380a

20x-10x+380a-90a=0

10x+290a=0

10(x+29a)=0

x+29a=0

30th term=0

Answer 2

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✤ Required Answer:

✒ GiveN:

• 10 times 10th term = 20 times 20th term

✒ To FinD:

• Find its 30 th term...?

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✤ How to Solve?

The above question is of AP, Arithmetic progression. Before solving the question, let's know something about arithmetic progression.

• Arithmatic progression is a type of sequence with numbers(terms) where difference between consecutive terms is constant.
• This difference is known as Common difference. This is helpful to prove whether a sequence is a AP.or not.
• General general of AP is a, a + d, a + 2d, a + 3d....Where a = First term, and d = common difference.

☯️ For finding the nth term of AP, Formula:

$\large{ \boxed{ \sf{a_n = a + (n - 1)d}}}$

Where, n is the number of terms.th

So, By using this formula, Let's solve the question...

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✤ Solution:

Let,

• a = first term
• d = common difference

Then, 10th term,

➙ a10 = a + (10 - 1)d

➙ a10 = a + 9d

&

And, 20th term,

➙ a20 = a + (20 - 1)d

➙ a20 = a + 19d

Given, ATQ

➙ 10(a + 9d) = 20(a + 19d)

➙ 10a + 90d = 20a + 380d

➙ 20a - 10a = 90d - 380d

➙ 10a = -290d

➙ 10a + 290d = 0

➙ 10(a + 29d) = 0

➙ a + 29d = 0

To find, 30th term

➙ a30 = a + (30 - 1)d

➙ a30 = a + 29d

And, we got that,

➙ a + 29d = 0

➙ a30 = 0

✒ 30th term of the AP = 0

☀️ Hence, solved !!

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