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Let a1 = 1 and am+n = am + an + 2mn for all positive integers m and n. Find a8.

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Let a1 = 1 and am+n = am + an + 2mn for all...

Let a1 = 1 and am+n = am + an + 2mn for all positive integers m and n. Find a8.

asked Apr 17, 2019 in order of operations by anonymous

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1 Answer

Let’s see what’s happening here.

We have a₁=1, so, to find a₂ m=n=1, and a₂=a₁+a₁+2=4.

Next, a₃ implies that m=2 and n=1, or m=1 and n=2, so a₃=4+1+4=9.

a₄=a₂+a₂+8=16. Also, a₄=a₁+a₃+6=10+6=16.

a₈=a₄+a₄+32=32+32=64.

answered Apr 17, 2019 by Rod Top Rated User (1.2m points)

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