A question on sequences and series

Question

anonymous · Answer

If $$\huge a _{1} , a _{2} , a _{3} , a _{4} , a _{5}$$
are in A.P with a common difference not equal to zero , 
then find the value of $$\sum_{i=1}^{5}a _{i}$$,
when $$a _{3} =2 $$

@ganeshie8 
I don't know what this question means

unklerhaukus · Answer

An arithmetic progression is a sequence, of which the difference between subsequent terms is constant ,



for example
the sequence is 2, 7, 12, 17, 22, 27, ...

 the first term is 2 and the common difference is 5,

anonymous · Answer

I know what A.P means but not the question and the sigma notation i am new to that symbol

kanwal32 · Answer

http://www.meritnation.com/ask-answer/question/a-2m-wide-truck-is-moving-with-a-uniform-speed-u-8-m-s-along/motion-in-a-plane/6152421

unklerhaukus · Answer

$$\sum_{i=1}^{5}a _{i}$$
means a sum of `a_i' terms,   where the first term is `a_1' and the last term is `a_5'

where `i' is integers 

in other words

$$\sum_{i=1}^{5}a _{i}=a_1+a_2+a_3+a_4+a_5$$

anonymous · Answer

they aren't giving you the difference?

kanwal32 · Answer

the answer that meritnation has given  is wrong in my textbook it is given is 1.6sqrt5 plshelp

anonymous · Answer

No @wio OK @UnkleRhaukus

unklerhaukus · Answer

the first term is a_1
i suppose you could say the common difference is 'd'

so  that a_2 = a_1+d

and    a_3 = a_2+d = a_1+d+d = a_1+2d

unklerhaukus · Answer

can you express the series in terms of a_3 and d?

anonymous · Answer

It is a example problem and it has a sollution but i don't understand it i would type wait

anonymous · Answer

As a_1 , a_2 ..... a_5 are in A.P, we have 
a_1 + a_5 = a_2 +a_4 = 2a_3
Hence 
$$\sum_{i=1}^{5}a _{i} = 10 $$

kanwal32 · Answer

A1=a-2d A3=a
A2=a-d A4=a+d and A5=a+2d

kanwal32 · Answer

a4-a3=a3-a2

anonymous · Answer

No

kanwal32 · Answer

4=2a+4d

unklerhaukus · Answer

a_1                      ->    a_1 = a_3-2d
a_2 = a_1+  d     ->    a_2 = a_3-d
a_3 = a_1+2d
a_4 = a_1+3d      ->    a_4 = a_3+d
a_5 = a_1+4d      ->    a_5 = a_3+2d

a_1+a_2+a_3+a_4+a_5 = (a_3-2d) + (a_3-d) + a_3 + (a_3+d) +(a_3+2d)
                                      = 5a_3

anonymous · Answer

so , 10 okay!

unklerhaukus · Answer

notice how the value of 'd ' doesn't matter because we know the middle term, (differences above and below cancel out )

unklerhaukus · Answer

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