Find the indicated terms of the sequences whose nth terms are given b

1.	Find the indicated terms of the sequences whose nth terms are given by(i) an = 5n/(n + 2); a6 and a13(ii) an = – (n2 – 4); a4 and a11
Answer» (i) a_n = 5n/(n + 2) a₆ = 5(6)/(6 + 2) = 30/8 = 15/4 a₁₃ = 5(13)/(13 + 2) = (5 x 13)/15 = 13/3 a₆ = 15/4, a₁₃ = 13/3 (ii) a_n = -(n² – 4) a₄ = -(4² – 4) = – (16 – 4) = -12 a₁₁ = -(11² – 4) = – (121 – 4) = – 117 a₄ = -12 and a₁₁ = -117

Find the indicated terms of the sequences whose nth terms are given by(i) an = 5n/(n + 2); a6 and a13(ii) an = – (n2 – 4); a4 and a11

Answer»

(i) a_n = 5n/(n + 2)

a₆ = 5(6)/(6 + 2) = 30/8 = 15/4

a₁₃ = 5(13)/(13 + 2) = (5 x 13)/15 = 13/3

a₆ = 15/4, a₁₃ = 13/3

(ii) a_n = -(n² – 4)

a₄ = -(4² – 4)

= – (16 – 4)

= -12

a₁₁ = -(11² – 4)

= – (121 – 4)

= – 117

a₄ = -12 and a₁₁ = -117