Question

Find the sum the first 5 terms of a G.P whose first term is 3 and its common ratio is 0.25 to 4s.f. ​

Answer 1

A G.P is a sequence of numbers such that the ratio of any two consecutive terms is a constant, called the common ratio. Given the first term (3) and the common ratio (0.25) of the G.P, we can find the sum of the first 5 terms using the formula:

S_n = a(1 - r^n) / (1 - r)

Where:

S_n is the sum of the first n terms of the G.P.

a is the first term of the G.P.

r is the common ratio of the G.P.

n is the number of terms in the sum.

So, to find the sum of the first 5 terms of the G.P, we can substitute the given values into the formula:

S_5 = 3(1 - (0.25)^5) / (1 - 0.25)

S_5 = 3(1 - (0.25)^5) / (1 - 0.25) = 3(1 - 0.25^5) / (1 - 0.25) = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75

S_5 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75

S_5 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.

Answer 2

3.996

Explanation:

`\boxed{\begin{minipage}{7 cm}\underline{Sum of the first $n$ terms of a geometric series}\\\\$S_n=(a(1-r^n))/(1-r)$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}`

Given:

• a = 3
• r = 0.25
• n = 5

Substitute the given values into the formula to find the sum of the first 5 terms of a geometric progression whose first term is 3 and common ratio is 0.25:

`\implies S_5=(3(1-0.25^5))/(1-0.25)`

`\implies S_5=(3(1-0.00097656...))/(0.75)`

`\implies S_5=(3(0.999023437...))/(0.75)`

`\implies S_5=(2.99707031...)/(0.75)`

`\implies S_5=3.99609375`

`\implies S_5=3.996\; \sf (4\;s.f.)`