Question

Find the 20th term of the sequence: 9, 5, 1, -3....

Answer 1

ANSWER:

20th term of the AP is -67.

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EXPLANATION:

Here this is a question from Arithmetic Progression, we have given an AP and we have to find the 20th term. So, to find the 20th term we have to apply formula for 20th term and put the given values.

So let's start!

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GIVEN AP:

9,5,1,-3...

First term, A=9

Common difference, d=A2-A1

Common difference, d=5-9

Common difference, d=-4

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TO FIND:

20th term

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SOLUTION:

We have formula for nth terms:

An=A+(n-1)d

Now put the given values

→ A20=9+(20-1)(-4)

→ A20=9+19(-4)

→ A20=9-76

→ A20=-67

So the required 20th term of the AP is -67.

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Answer 2

To Find:-

• The 20th term of the sequence: 9,5,1,-3 ... .

Solution:

Given:

• Given, sequence: 9, 5, 1, -3 .... .

Step-by-step explanation:

Here, given sequence is an A.P. with the first term ( a = 9 ), The common difference is :-

• 5 - 9 = -4
• 1 - 5 = -4
• - 3 - 1 = -4

So, The common difference is -4.

According the question,

The 20th term of A.P. is :-

⟹ tₙ = a + ( n - 1 ) d

Where,

• tₙ = nth term
• a = first term
• n = number of terms
• d = common difference.

Therefore,

⟹ t₂₀ = 9 + ( 20 - 1 ) - 4

⟹ t₂₀ = 9 + 19 × - 4

⟹ t₂₀ = 9 + - 76

⟹ t₂₀ = 9 - 76

⟹ t₂₀ = -67

Hence, The 20th term of A.P. is -67.

Required Answer:-

• The 20th term of the sequence: 9,5,3,-1 ... . is -67.