Yes, 23 has an inverse mod 1000 because gcd(23, 1000) = 1 (i.e. they are coprime).
Let <em>x</em> be the inverse. Then <em>x</em> is such that
23<em>x</em> ≡ 1 (mod 1000)
Use the Euclidean algorithm to solve for <em>x</em> :
1000 = 43×23 + 11
23 = 2×11 + 1
→ 1 ≡ 23 - 2×11 (mod 1000)
→ 1 ≡ 23 - 2×(1000 - 43×23) (mod 1000)
→ 1 ≡ 23 - 2×1000 + 86×23 (mod 1000)
→ 1 ≡ 87×23 - 2×1000 ≡ 87×23 (mod 1000)
→ 23⁻¹ ≡ 87 (mod 1000)
Answer:
see explanation
Step-by-step explanation:
To calculate the first 3 terms substitute n = 1, 2, 3 into the n th term rule
= (3 × 1) + 2 = 3 + 2 = 5
= (3 × 2) + 2 = 6 + 2 = 8
= (3 × 3) + 2 = 9 + 2 = 11
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substitute n = 10 into the n th term rule
= (3 × 10) + 2 = 30 + 2 = 32
Answer:
B
Step-by-step explanation:
1.6/0.2=8
10⁵-10²=10³
Answer:
=
+ 6
Step-by-step explanation:
The terms have a common difference d between consecutive terms, that is
10 - 4 = 16 - 10 = 22 - 16 = 6
To obtain the next term add 6 to the previous term ( recursive rule ), thus
=
+ 6 with a₁ = 4
Answer:
Step-by-step explanation:
area becomes 2²=4 times.