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.

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

yor answer is 7/6 times 5

step-by-step explanation:

the answer is thin because within context, the stanza concludes the and frail tone the people have toward each other, and the fact that it would be thin, makes the most sense compared to "pliable" or "not hard or firm to the touch". hope this , good luck.

step-by-step explanation:

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