For a sequence Sn = 4(7n – 1), verify whether the sequence is a G.P. - Mathematics and Statistics

Sum

For a sequence Sn = 4(7n – 1), verify whether the sequence is a G.P.

Solution

Sn = 4(7n – 1)

∴ Sn–1 = 4(7n–1 – 1)

But, tn = Sn – Sn–1

= 4(7n – 1) – 4(7n–1 – 1)

= 4(7n – 1– 7n– 1 + 1)

= 4(7n–1+1 – 7n–1)

= 4.7n–1 (7 – 1)

∴ tn = 24.7n–1

∴ tn+1 = 24(7)n+1–1

= 24(7)n

The sequence (tn) is a G.P., if ("t"_("n" + 1))/"t"_"n" = constant for all n ∈ N.

∴ ("t"_("n" + 1))/"t"_"n" = (24(7)^"n")/(24(7)^("n" - 1)

= 7 = constant, for all n ∈ N

∴ the sequence is a G.P.

Concept: Sequence and Series - Geometric Progression (G.P.)
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Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 4 Sequences and Series
Miscellaneous Exercise 4 | Q 7 | Page 64