Question

an =3n+1 in the arithmetic progression then the 3rd term is
options :a)9. b) 28. c)4. d)10
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Answer 1

Answer:

10

Step-by-step explanation:

3(3)+1

9+1

10

hope it helps

Answer 2

Required Answer :

Option d) 10

The third term of A.P. = 10

Step by step explanation :

We have :

→ A.P = 3n + 1

To find :

→ The third term of A.P.

Solution :

We can solve this question by two methods.

First method :

Substitute 3 in place of n :

⇒ 3n + 1

⇒ 3(3) + 1

⇒ 9 + 1

⇒ 10

Therefore, the third term of A.P. = 10

Second method :

Firstly, substitute 1 and 2 in place of n and calculate the common difference.

First term :

⇒ 3n + 1

⇒ 3(1) + 1

⇒ 3 + 1

⇒ 4

First term = 4

Second term :

⇒ 3n + 1

⇒ 3(2) + 1

⇒ 6 + 1

⇒ 7

Second term = 7

• Common difference (d) = Second term - First term

⇒ Common difference = 7 - 4

⇒ Common difference = 3

Now, by using the follow formula, we can calculate the third term of A.P. :

⇒ tₙ = a + (n - 1)d

where,

• a = First term
• n = Number of terms
• d = Common difference

Substituting the given values :

⇒ t₃ = 4 + (3 - 1)3

⇒ t₃ = 4 + (2)3

⇒ t₃ = 4 + 6

⇒ t₃ = 10

Therefore, the third term of A.P. = 10