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
You might be interested in
The surface area of the square pyramid is 360 in²
Explanation:
Given that the side length is 10 inches.
The height of the pyramid is 12 inches.
We need to determine the surface area of the pyramid.
The surface area of the pyramid is given by
Where s is the side length and l is the slant height.
The slant height can be determined using the formula,
where h = 12 and
Substituting these values in the formula, we get,
Thus, the slant height is
Now, we shall find the surface area of the pyramid.
Substituting and
in the formula
, we get,
Thus, the surface area of the square pyramid is 360 in²