Find the seventh term of the following sequence. 2/9, 2/3, 2,…….

1.	Find the seventh term of the following sequence. 2/9, 2/3, 2,…….
Answer» \(\frac{2}{9}, \frac{2}{3}, 2,.....\) Given sequence is a geometric progression. whose first term a \(=\frac{2}{9}\) Common ratio r \(=\frac{a_2}{a_1}\) \(=\frac{\frac{2}{3}}{\frac{2}{9}}=\frac{2}{3}\times \frac{9}{2}\) = 3 \(\therefore\) \(7^{th}\) term of G.P is \(a_7 = ar^{7-1}=ar^6\) \(=\frac{2}{9}\times 3^6=2\times 3^4\) \(=2\times 81\) = 162.

Answer»

\(\frac{2}{9}, \frac{2}{3}, 2,.....\)

Given sequence is a geometric progression.

whose first term a \(=\frac{2}{9}\)

Common ratio r \(=\frac{a_2}{a_1}\) \(=\frac{\frac{2}{3}}{\frac{2}{9}}=\frac{2}{3}\times \frac{9}{2}\) = 3

\(\therefore\) \(7^{th}\) term of G.P is \(a_7 = ar^{7-1}=ar^6\)

\(=\frac{2}{9}\times 3^6=2\times 3^4\)

\(=2\times 81\)

= 162.

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