Question

If an = n(n – 3)/ n + 4, then find 18th term of this sequence.​

Answer 1

Answer:

Step-by-step explanation: n means the position of the term

if (1st position)1st term(n) = 1

given : a(n) = n(n-3)/n+4

a1  = 1(1-3)/1+4 =

a1  = -2/5

if (1st position)1st term(n) = 1

a2 = 2(2-3)/2+4 = -2/6 = -1/3

d(common difference) = a2-a1

d = -1/3 - (-2/5)

d = -1/3 + 2/5

Taking L.C.M,

d = -1*5/3*5 + 2*3/5*3

d = -1/15 + 6/15

d = 5/15

d = 1/3

so,

t18 = a(1st term) + (n-1)*d

t18 = -2/5 + (n-1)*1/3

t18 = -2/5 + (n-1)/3

t18 = -2*3/5*3 + (n-1)*5/3*5

t18 = -6/15 + (5n-5)/13

t18 = -6+5n-5/15

t18 = -11+5n/15

t18 = -11+5(18)/15 as n = 18

t18 = -11+5(18)/15

t18 = -11+90/15

t18 = -79/15

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Answer 2

Answer:

If an = n(n – 3)/ n + 4, then find 18th term of this sequence.