Question

Find a formula for the general term of the sequence { 5/3, - 6/9, 7/27, - 8/81, 9/243, ... } assuming that the pattern of the first few terms continues. SOLUTION We are given that a1 = 5/3 a2 = - 6/9 a3 = 7/27 a4 = - 8/81 a5 = 9/243 Notice that the numerators of these fractions start with 5 and increase by 1 whenever we go to the next term. The second term has numerator 6, the third term has numerator 7; in general, the nth term will have numerator n + 2. The denominators are powers of 3, so an has denominator 3^n. The signs of the terms are alternately positive and negative so we need to multiply by a power of -1. Here we want to start with a positive term and so we use (-1)^(n - 1) or (-1)^(n + 1). Therefore, an = (-1)^(n - 1) * ( (n + 2) / 3^n )

          Find a formula for the general term of the sequence
{ 5/3, - 6/9, 7/27, - 8/81, 9/243, ... }
assuming that the pattern of the first few terms continues.

SOLUTION We are given that
a1 = 5/3 a2 = - 6/9 a3 = 7/27 a4 = - 8/81 a5 = 9/243

Notice that the numerators of these fractions start with 5 and increase by 1 whenever we go to the next term. The second term has numerator 6, the third term has numerator 7; in general, the nth term will have numerator n + 2. The denominators are powers of 3, so an has denominator 3^n. The signs of the terms are alternately positive and negative so we need to multiply by a power of -1. Here we want to start with a positive term and so we use (-1)^(n - 1) or (-1)^(n + 1). Therefore,
an = (-1)^(n - 1) * ( (n + 2) / 3^n )

$Find a formula for the general term of the sequence 5/3, - 6/9, 7/27, - 8/81, 9/243, ... assuming that the pattern of the first few terms continues. SOLUTION We are given that a1 = 5/3 a2 = - 6/9 a3 = 7/27 a4 = - 8/81 a5 = 9/243 Notice that the numerators of these fractions start with 5 and increase by 1 whenever we go to the next term. The second term has numerator 6, the third term has numerator 7; in general, the nth term will have numerator n + 2. The denominators are powers of 3, so an has denominator 3^n. The signs of the terms are alternately positive and negative so we need to multiply by a power of -1. Here we want to start with a positive term and so we use (-1)^(n - 1) or (-1)^(n + 1). Therefore, an = (-1)^(n - 1) * ( (n + 2) / 3^n )$

Added by Dawn F.

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