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Simplifying a(n) = 2a(n + -1) + n + 5 Multiply a * n an = 2a(n + -1) + n + 5 Reorder the terms: an = 2a(-1 + n) + n + 5 an = (-1 * 2a + n * 2a) + n + 5 an = (-2a + 2an) + n + 5 Reorder the terms: an = 5 + -2a + 2an + n Solving an = 5 + -2a + 2an + n Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2a' to each side of the equation. 2a + an = 5 + -2a + 2an + 2a + n Reorder the terms: 2a + an = 5 + -2a + 2a + 2an + n Combine like terms: -2a + 2a = 0 2a + an = 5 + 0 + 2an + n 2a + an = 5 + 2an + n Add '-2an' to each side of the equation. 2a + an + -2an = 5 + 2an + -2an + n Combine like terms: an + -2an = -1an 2a + -1an = 5 + 2an + -2an + n Combine like terms: 2an + -2an = 0 2a + -1an = 5 + 0 + n 2a + -1an = 5 + n Reorder the terms: -5 + 2a + -1an + -1n = 5 + n + -5 + -1n Reorder the terms: -5 + 2a + -1an + -1n = 5 + -5 + n + -1n Combine like terms: 5 + -5 = 0 -5 + 2a + -1an + -1n = 0 + n + -1n -5 + 2a + -1an + -1n = n + -1n Combine like terms: n + -1n = 0 -5 + 2a + -1an + -1n = 0 The solution to this equation could not be determined.
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