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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

term is 86.

1 Answer

2 votes

Answer:f(n) = 12n + 1

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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