Find a5 for the arithmatic sequence a1=1 and a3=25

Question

unklerhaukus · Answer

$$a_1=1$$$$a_2=\frac{1+25}2$$$$a_3=25$$
$$a_n=(a_2-a_1)n=(a_3-a_2)n$$

anonymous · Answer

whats n

unklerhaukus · Answer

$n$ is the position of the term in the sequence 
$a_1$ is the first term,
$a_2$ is the second term,
$a_5$ is the fifth term
$a_n$ is the $n$-th term

anonymous · Answer

so n is 5

anonymous · Answer

It will be easy if you find Arithmetic Mean first..

anonymous · Answer

$$AM = a_2 = \frac{a_1 + a_3}{2} \implies \frac{1 + 25}{2} \implies a_2 = 13$$

anonymous · Answer

Solution:
a1=1

  a3 = 25
 a+2d = 25
 2d = 24
 d = 12

a5 = a + 4d
     = 1 + (4*12)
     = 49. Ans

anonymous · Answer

@curiousshubham Perhaps you shouldn't have given the direct answer to the question?

anonymous · Answer

Now you can easily find common difference here:
$$d = a_2 - a_1 = 13 - 1 = 12$$

anonymous · Answer

@RolyPoly How I am supposed to provide the answer?

anonymous · Answer

And fifth you can find as:

$$a_5 = a_1 + (5-1)(d)$$

anonymous · Answer

According to the Code of Conduct ( http://openstudy.com/code-of-conduct) Give Help, , Not Answers. @curiousshubham

anonymous · Answer

@RolyPoly  sorry for that...

a5 is the 5th term and accroding to question the value of 1st and 3rd term is 1 and 25 respectively. So all you need to do is find the term difference using the given terms i.e. 1st and 3rd. And then use the formula:
   nth term = a + (n-1)d.