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## SS2: MATHEMATICS - 2ND TERM

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Lesson 3, Topic 2
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# The Sum of Nth Term of a G.P

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#### Topic Content:

• The Sum of Nth Term of a G.P

Finding the sum of terms in a geometric progression can be obtained with the use of formulas.

The sum of the first nth term of a G.P is given as

Sn = $$\frac{a(r^n \: – \: 1)}{r \: – \: 1}$$ (r > 1)

or

Sn = $$\frac{a(1 \: – \: r^n)}{1 \: – \: r}$$  (r < 1)

### Sum of a G.P to Infinity:

The sum to infinity of a geometric series,

S = $$\frac{a}{1 \: – \: r}$$ (-1<r<1)

### Example 3.2.1:

If the 2nd and 5th terms of a G.P are -6 and 48 respectively, Find the sum of the first four terms. (SSCE)

Solution

T2 = ar = -6 ……….(1)

T5 = ar4 = 48 ……….(2)

divide equation (2) by equation (1)

⇒ $$\frac {ar^4}{ar} = \frac {48}{-6}$$

r3 = -8

take the cube root of both sides

$$\scriptsize \sqrt[3]{r^3} = \sqrt[3]{-8}$$

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