Question

Find the next term of the
5, 6, 12, 40, 190 -
series​

Answer 1

Answer:

1128

Step-by-step explanation:

5×2=10-4 =6

6×3=18-6 =12

12×4=48-8=40

40×5=200-10=190

190×6=1140-12=1128

Answer 2

Answer:

The next term of the 5, 6, 12, 40, 190 , .. = 1128

Step-by-step explanation:

Given sequence is

5, 6, 12, 40, 190 , ....

To find,

The 6th term of this sequence

Solution:

First term = t₁ = 5

Second term = t₂= 6 = 5×2 -2×2 = 2×(t₁ -2)

Third term = t₃ = 12 =  6×3 - 3×2 = 3×(t₂ -2)

Fourth term = t₄ = 40 = 12×4 - 4×2 = 4×( t₃ -2)

Fifth term = t₅ = 190 = 40×5 - 5×2 = 5×( t₅ -2)

Hence we have

t₂= 2×(t₁ -2)

t₃ = 3×(t₂ -2)

t₄ = 4×( t₃ -2)

t₅ = 5×( t₅ -2)

Continuing like this we get the nth term of this sequence as

tₙ= n×(tₙ₋₁ -2)

Substituting n = 6 , we get

Sixth term = t₆ = 6×(t₅ -2)

= 6×(190 -2)

= 1128

∴Sixth term = t₆= 1128

The next term of the 5, 6, 12, 40, 190 , .. = 1128

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