4
th Term of an arithmetic sequence is 23 and its 11th term is 65
a) What is its common difference ?
b) What is its first term ?
c) What is its algebraic form ?
Answers
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Answer:
- common difference = d = 6
- first term = x₁ = 5
- algebric form = 6n-1
Step-by-step explanation:
QUESTION:-
4th Term of an arithmetic sequence is 23 and its 11th term is 65
TO FIND:-
a) What is its common difference ?
b) What is its first term ?
c) What is its algebraic form ?
WE HAVE:-
T₄ = 3
T₁₁ = 65
SOLUTION:-
4'TH TERM ⇒ A + 3D = 23 ----------(1)
11'TH TERM⇒ A + 10D = 65 ---------(2)
WE HAVE TO FIND FIRST TERM AND COMMON DIFFERENCE FOR THIS WE HAVE TO SOLVE EQN (1)&(2)
A + 3D = 23
A + 10D = 65
SOLVE ,WE GET -7D = -42
⇒ D = 6
PUT D IN EQN (1) OR(2)
A + 3D = 23
A + 18 = 23
=> A = 5
ALGEBRIC FORM
⇒ A + (n-1)D
⇒5 + (n-1)6
⇒5 + 6n-6
⇒6n-1
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