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Question Number 43072 by Raj Singh last updated on 07/Sep/18

	Answered by tanmay.chaudhury50@gmail.com last updated on 07/Sep/18
	$3^(50) (3^(49) −1) 3^1 →unit term is 3 3^2 →unit term is9 3^3 →unit term is 7 3^4 →unit term is1 3^5 →unit term is 3 so sequence is 3 9 7 1 3 9 7 1 now 3^(50) (3^(49) −1) (3^4 )^(12) ×3^2 {(3^4 )^(12) ×3−1} unit term for 3^(48) →(3^4 )^(12) is1 unit term of 3^(48) ×3^2 →9 unit term of (3^4 )^(12) ×3→3 unit term of (3^4 )^(12) ×3−1 →2 so unit term of (3^4 )^(12) ×3^2 {(3^4 )^(12) ×3−1} is→8$
	$3^{50} (3^{49} - 1)$ $3^{1} \to u n i t t e r m i s 3$ $3^{2} \to u n i t t e r m i s 9$ $3^{3} \to u n i t t e r m i s 7$ $3^{4} \to u n i t t e r m i s 1$ $3^{5} \to u n i t t e r m i s 3$ $s o s e q u e n c e i s 3 9 7 1 3 9 7 1$ $n o w$ $3^{50} (3^{49} - 1)$ ${(3^{4})}^{12} \times 3^{2} {{(3^{4})}^{12} \times 3 - 1}$ $u n i t t e r m f o r 3^{48} \to {(3^{4})}^{12} i s 1$ $u n i t t e r m o f 3^{48} \times 3^{2} \to 9$ $u n i t t e r m o f {(3^{4})}^{12} \times 3 \to 3$ $u n i t t e r m o f {(3^{4})}^{12} \times 3 - 1 \to 2$ $s o u n i t t e r m o f$ ${(3^{4})}^{12} \times 3^{2} {{(3^{4})}^{12} \times 3 - 1} i s \to 8$
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