Given that a6 + a9 = 90 - a1 determine a1 + a2 +..+ a10 if a1, a2, ... are the terms of an a.p.

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a6+a9 = 90 = a1

we know that:

a6 = a2+4r

==> a2+4r + a9 = 90-a1

==> a1+a2 + a9 + 4r = 90

==> a1+ a2 + a9 = 90-4r .......(1)

Now we need the values of:

a1+a2 + a10 = ??

a10 = a9 + r

==> a1 + a2 + a10 = a1 + a2 + a9 + r

              From (1) :

                               = 90-4r + r

                                = 90-3r

 

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