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