Question

if the 5th term and 21st term of an ap are 14 and -14 respectively then which term of the ap is zero

Answer 1

Answer:

If the 5th term and 21st term of an ap are 14 and -14 respectively then 13th term of the ap is zero.

Step-by-step explanation:

Formula : nth term = a + ( n - 1 )d, where a is first term and d is common difference.

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

→ 5th term = 14

→ a + 4d = 14

→ a = 14 - 4d ---(1)

→ 21st term = - 14

→ a + 20d = - 14

From (1),

→ 14 - 4d + 20d = - 14

→ 16d = - 14 - 14

→ 16d = - 28

→ d = - 28/16

→ d = - 7/4

So,

→ a = 14 - 4(-7/4)

→a = 14 + 7

→ a = 21

Let xth term be 0, so

→ 0 = 21 + ( x - 1 )(-7/4)

→ - 21 = ( x - 1 )(-7/4)

→ 21 = (x-1)(7/4)

→ ( 21 * 4 / 7 ) = x - 1

→ 12 = x - 1

→ 13 = x

13th term is 0.

Answer 2

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If the 5th term and 21st term of an ap are 14 and -14 respectively then which term of the ap is zero.

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★ Given that,

• a5 = 14
• a21 = - 14

★ To find,

• Which term of the AP will be zero...?

★ Let,

\sf\: a_{5} = a + 4d = 21 ..... ➊

$\sf\: ↪ a_{5} = a + 4d = 14 ..... ➊$

$\sf\:↪ a_{21} = a + 20d = - 14 ..... ➋$

From the equations ➊ & ➋, we get...

$\sf\:⟹ 16d = - 28$

$\sf\:⟹ d = \frac{-28}{16}$

$\sf\:⟹ d = \frac{-7}{4}$

$\boxed{∴ d = \frac{-7}{4}}$

• Substitute the value of d ➊.