Question

is 101 a term of the sequence 3,7,11. then what about 103?​

Answer 1

Answer:

101 is not the term of the AP and 103 is the term of the A.P

Step-by-step explanation:

Given A.P → 3, 7, 11, ...

We need to find whether 101 and 103 are a term in this sequence or not.

First, consider 101:

In the AP

• a = 3
• d = 7 - 3 = 4
• aₙ = 101

We know that:

  aₙ = a + (n - 1)d

⇒ 101 = 3 + (n - 1)4

⇒ 4 (n - 1) = 98

⇒ (n - 1) = 24.5

⇒ n = 25.5

'n' cannot be a fraction.

So, 101 is not the term of the A.P

Now consider 103;

In the A.P

• a = 3
• d = 7 - 3 = 4
• aₙ = 103

Again,

  aₙ = a + (n - 1)d

⇒ 103 = 3 + (n - 1)4

⇒ 100 = 4(n - 1)

⇒ (n - 1) = 100 ÷ 4

⇒ (n - 1) = 25

⇒ n = 26

∴ 26th term of the A.P is 103.