Question 1199651
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The sum of the first four terms of a linear sequence A.p is 26 
and that of the next four term is 74. 
find the value of the first term ,the common difference
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<pre>
We are given

    {{{a[1]}}} + {{{a[2]}}} + {{{a[3]}}} + {{{a[4]}}} = 26,    (1)

    {{{a[5]}}} + {{{a[6]}}} + {{{a[7]}}} + {{{a[8]}}} = 74.    (2)


It is the same as

    {{{4*a[1]}}} + (1+2+3)d   = 26,     

    {{{4*a[1]}}} + (4+5+6+7)d = 74,

or

    {{{4*a[1]}}} +  6d = 26,   (3)

    {{{4*a[1]}}} + 22d = 74.   (4)


From (4), subtract (3).  You will get

    22d - 6d = 74 - 26 

       16d   =    48

         d   =    48/16 = 3.


Thus the common difference of this AP is 3.


Next, from (3)

    {{{4*a[1]}}} = 26 - 6*3 = 26 - 18 = 8,

    {{{a[1]}}} = 8/4 = 2.


<U>ANSWER</U>.  The first term of the AP is 2;  the common difference is 3.


<U>CHECK</U>.  Use equation (4) to check this answer ON YOUR OWN.
</pre>

Solved.