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Sunny_sXe [5.5K]
3 years ago
5

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

Mathematics
1 answer:
Westkost [7]3 years ago
7 0

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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