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(1)
an =a1.q^(n-1)
(a5)^2 = a10
a1^2.q^8 = a1.q^9
a1= q
2[ an+a(n+2) ] = 5a(n+1)
2[ q^n +q^(n+2) ] = 5q^(n+1)
2[ 1 +q^2 ] = 5q
2a^2 -5q+2 =0
(2q-1)(q-2) =0
q=2
=> an = 2^n
(2)
2^(11) =2048
cn = 1-(-1)^n.an
= 1-(-1)^n.2^n
ck ≥ 2014
c11,c13,c15,.,c99 ≥ 2014
c11+c13+c15+.+c99
=45 + ( 2^11+2^13+.+2^99)
=45 + [ 2^11( 2^90 -1) /3 ]