Question

The sum of the terms of an infinite geometric progression is 35 and the common ratio is 2 5 . What is the first term of the progression?

Answer 1

Answer:

The first term of geometric progression is 21.

Step-by-step explanation:

We are given the following in the question:

The sum of the terms of an infinite geometric progression is 35.

Common ratio = $\frac{2}{5}$

Sum of an infinite GP =

$\displaystyle\frac{a}{1-r}$

where a is the first term of GP and r is the common ratio.

Puting the values, we get,

$35 = \displaystyle\frac{a}{1-\frac{2}{5}}\\\\a = 35\times (1-\frac{2}{5})\\\\a = 35\times \frac{3}{5}\\\\a = 21$

Thus, the first term of geometric progression is 21.

Answer 2

The first term of the infinite geometric progression is 21

Sum of infinite geometric progression

• First term = a
• common ratio = 2/5
• Sum = 35

Sum of infinite geometric progression = a / (1 - r)

35 = a / (1 - 2/5)

35 = a / ( 5-2 / 5)

35 = a / 3/5

cross product

35 × 3/5 = a

105/5 = a

a = 21

Therefore, the first term of the infinite geometric progression is 21

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