Question

The first terms of a geometric sequence are as follows.

Answer 1

The fourth and fifth term of this sequence is -30 and -10 respectively.

Data;

• first term (a) = -810
• common difference (r) = ?

Common Difference

The common difference in a geometric progression is the ratio between two successive terms.

Let's find the common difference in this sequence

$r = \frac{-270}{-810} \\r = \frac{1}{3}$

The nth term of a geometric sequence is given as

$T_n = ar^n^-^1$

The next two terms of this sequence will be 4th and 5th term.

The fourth term of this sequence is

$T_4 = ar^4^-^1\\T_4 = -810 * (\frac{1}{3})^3\\ T_4 = -810 * \frac{1}{27}\\ T_4 = -30$

The fifth term of this sequence is

$T_5 = ar^5^-^1\\T_5 = -810 * (\frac{1}{3})^4\\T_5 = -810 * \frac{1}{81} \\T_5 = -10$

The fourth and fifth term of this sequence is -30 and -10 respectively.

Learn more on geometric progression here;

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