Find an explicit form f(n) of the arithmetic sequence where the 2nd term is 25 and the sum of the 3rd term and 4th
1 answer:
Answer:f(n) = 12n + 1
Step-by-step explanation:
Since it is an arithmetic sequence, the general formula for nth term is given as
f(n) = a + ( n-1)d , where a is the first term, n is the number of terms and d is the common difference.
Given from the question
Second term is 25 , which means that
a + d = 25
Also given , the sum of third and fifth term is 86, which means
a + 2d + a + 3d = 86
2a + 5d = 86
Combining the two equations , we have
a + d = 25 ………….. I
2a + 5d = 86………..II
Using substitution method to solve the resulting simultaneous equation
From equation I make a the subject of the formula, which gives
a = 25 – d…………………. III
Substitute the value of a into equation II , we have
2 ( 25 – d) + 5d = 86
Expanding
50 + 2d + 5d = 86
50 + 3d = 86
Collect the like terms
3d = 86 – 50
3d = 36
d = 12
substitute the value of d into equation III, we have
a = 25 – 12
a = 13
Since we have gotten the value of a and b , we will substitute into the general formula for the nth term
f(n) = a + ( n-1)
f(n) = 13 + (n-1)12
Expanding
f(n) = 13+ 12n -12
f(n) =12n + 1
Therefore the explicit form f(n) of the arithmetic sequence is f(n) =12n + 1
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