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Let a1, a2, a3, be an A.P. and g1=a1, g2, g3, be an increasing G.P. If a1=a2+g2=1 and a3+g3=4, then a10+g5 is equal to:
(4) 55
a1=g1=1. Let the A.P. have common difference d and the G.P. common ratio q.
a2+g2=1 (1+d)+q=1 d=-q
a3+g3=4 (1+2d)+q2=4
q2-2q-3=0 (q-3)(q+1)=0
The G.P. is increasing, q=3 (not -1) d=-3
a10=1+9(-3)=-26, g5=34=81
a10+g5=-26+81=55
Answer: (4)
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