(4) In an A. P. if a = 2 and t⁵= 12,
find t², t³, t⁴.
Answers
Appropriate Question:
In an A.P. if first term = 2 and fifth term = 12, find the second term, third term and fourth term.
Answer:
- Second term = 4.5
- Third term = 7
- Fourth term = 9.5
Step-by-step explanation:
Given that:
In an A.P.
- First term = 2
- Fifth term = 12
To Find:
- Second term
- Third term
- Fourth term
Concept:
- First we have to find the common difference of the given A.P. after that we will able to find all these given terms.
Formula used:
- aₙ = a + (n - 1)d
Where,
- aₙ = nth term
- a = First term
- n = number of terms
- d = Common difference
Finding the common difference:
⟶ Fifth term = 12
⟶ 2 + (5 - 1)d = 12 [∵ a = 2]
⟶ 2 + 4d = 12
⟶ 4d = 12 - 2
⟶ 4d = 10
⟶ d = 10/4
⟶ d = 2.5
∴ Common difference = 2.5
Finding the following terms:
⇒ a₂ = 2 + (2 - 1)2.5
⇒ a₂ = 2 + (1)2.5
⇒ a₂ = 2 + 2.5
⇒ a₂ = 4.5
∴ Second term = 4.5
⇒ a₃ = 2 + (3 - 1)2.5
⇒ a₃ = 2 + (2)2.5
⇒ a₃ = 2 + 5
⇒ a₃ = 7
∴ Third term = 7
⇒ a₄ = 2 + (4 - 1)2.5
⇒ a₄ = 2 + (3)2.5
⇒ a₄ = 2 + 7.5
⇒ a₄ = 9.5
∴ Fourth term = 9.5
Appropriate Question:
In an A.P. if first term = 2 and fifth term = 12, find the second term, third term and fourth term.
Answer:
Second term = 4.5
Third term = 7
Fourth term = 9.5
Step-by-step explanation:
Given that:
In an A.P.
First term = 2
Fifth term = 12
To Find:
Second term
Third term
Fourth term
Concept:
First we have to find the common difference of the given A.P. after that we will able to find all these given terms.
Formula used:
aₙ = a + (n - 1)d
Where,
aₙ = nth term
a = First term
n = number of terms
d = Common difference
Finding the common difference:
⟶ Fifth term = 12
⟶ 2 + (5 - 1)d = 12 [∵ a = 2]
⟶ 2 + 4d = 12
⟶ 4d = 12 - 2
⟶ 4d = 10
⟶ d = 10/4
⟶ d = 2.5
∴ Common difference = 2.5
Finding the following terms:
⇒ a₂ = 2 + (2 - 1)2.5
⇒ a₂ = 2 + (1)2.5
⇒ a₂ = 2 + 2.5
⇒ a₂ = 4.5
∴ Second term = 4.5
⇒ a₃ = 2 + (3 - 1)2.5
⇒ a₃ = 2 + (2)2.5
⇒ a₃ = 2 + 5
⇒ a₃ = 7
∴ Third term = 7
⇒ a₄ = 2 + (4 - 1)2.5
⇒ a₄ = 2 + (3)2.5
⇒ a₄ = 2 + 7.5
⇒ a₄ = 9.5
∴ Fourth term = 9.5
Remark:
Hope this answer will help you.✌️