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Alpha Numeric Patterns

Finda T n and...

Question

Find

(a) T_n and T₈ for 1, 2, 4, 8, …….

(b) T₆ for

(c) T₉ for 1, 0.2, 0.02, 0.002, …….

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Solution

(a) The given sequence is 1, 2, 4, 8 …

Thus, the given sequence is in G.P.

In a G.P., .

(b) The given sequence is

In a G.P., .

∴

(c) The given sequence is

In s G.P., .

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Similar questions

Q. Determine two

G . P . s

which satisfy the following conditions:

T_{1} + T_{2} + T_{3} + T_{4} = 30

T_{5} + T_{6} + T_{7} + T_{8} = 480

Also prove the following for both:
(i)

S_{6} - S_{4} = 96

\frac{T_{n}}{T_{n}^{'}} = \frac{1}{3} {(- 1)}^{n}

Find

(a)

(b)

(c)

Find the G.P. if

(a) T₃ : T₆ = 1 : 8 and T₅ = 64

(b) T₄ : T8 = 1 : 81 and T₆ = 486

(c) S₁₀ : S₅ = 33 : 1 and T₆= 32

(d) S₈ : S₄ = 97 : 81 and T₅ = 16

x \in [- 3, 1),

\frac{1}{x^{3}}

t_{n} = \frac{1 + {(- 2)}^{n}}{n - 1}

t_{6} - t_{5}

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