Question

17. The third term an Arithmetic Progression whose fourth term is 9 and common difference is 2 is
a) 8 5) 7 C) 6 d) 5​

Answer 1

Answer:

the common difference is = 2

4th term is = 9

3rd term is ,= 4th term - common difference

= 9 - 7

= 2

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Answer 2

AnswEr :

• The third term of an arithmetic progression is 7.

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Given :

• Third term of an AP = Unknown.
• Fourth term of an AP = 9.
• Common difference of an AP = 2.

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Unknowable :

• Third term of an AP = ?

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Calculations :

Here is in this question we are provided with fourth term of an arithmetic progression and common difference of an arithmetic progression, and we are unknown with the third term of an arithmetic progression, so we need to find out the third term. To find the third term firstly we need to find out the first term of an arithmetic progression, after that we can easily calculate the third term. So let's start solving our problem and understanding the steps to get our final answer. Let's do it...!!

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We know that, if we are given with the fourth term and the common difference of AP, then we have the required formula, which says :

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a₄ = a + 3d.

[Here, a₄ denotes the third term, a denotes the first term and d denotes the common difference of an AP.]

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By using the required formula of AP and substituting the given values in the formula, we get:

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→ 9 = a + 3 * 2

→ 9 = a + 6

→ a = 9 - 6

→ a = 3

Now we have the first term of an AP, now we can easily calculate the third term of an AP.

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We know that, if we are given with the first term and the common difference of AP, then we have the required formula, which says :

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a₃ = a + 2d.

[Here, a₃ denotes the third term, a denotes the first term and d denotes the common difference of an AP.]

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By using the required formula of AP and substituting the given values in the formula, we get:

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→ a₃ = 3 + 2 * 2

→ a₃ = 3 + 4

→ a₃ = 7.

Hence, the third term of an arithmetic progression is 7.