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Answer :
The sequence is an arithmetic sequence
The solution is Option C.
The common difference is 10, so the function is f(n + 1) = f(n) + 10
where f(1) = 14.
What is Arithmetic Progression?
An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Given data ,
Let the arithmetic sequence be A = 14, 24, 34, 44, 54 ..
Now , the common difference between these numbers is calculated by
Common difference d = second term - first term
Common difference d = 24 - 14
Common difference d = 10
Now , let the number of terms be = n
The first term of the arithmetic sequence is f ( 1 ) = 14
The second term of the arithmetic sequence is f ( 2 ) = f ( 1 ) + d
f ( 2 ) = 14 + 10
f ( 2 ) = 24
The third term of the arithmetic sequence is f ( 3 ) = f ( 2 ) + 10
f ( 3 ) = 24 + 10
f ( 3 ) = 34
The fourth term of the arithmetic sequence is f ( 4 ) = f ( 3 ) + 10
f ( 3 ) = 34 + 10
f ( 4 ) = 44
So , the arithmetic progression is given by the equation
f ( n + 1 ) = f ( n ) + 10
where f ( 1 ) = 14 and the common difference d is 10
Hence , The common difference is 10, so the function is f(n + 1) = f(n) + 10 where f(1) = 14.
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