Question

I need help please actually give me the correct answer

Answer 1

Step-by-step explanation:

Given :-

First term is 10 and Common ratio is 0.25 of a GP

To find :-

I) Find the first four terms of the GP ?

ii) Find the sum of first 17 terms of the GP ? Round to the nearest tenth ?

Solution :-

Given that :

First term (a) = 10

Common ratio (r) = 0.25

We know that

The general form of a GP is a ,ar,ar²,ar³,...

a = 10

ar = 10×0.25 = 2.5

ar² = 10×(0.25)²

=> ar² = 10×0.0625

=> ar² = 0.625

ar³ = ar²×r

=> ar³ = 0.625×0.25

=> ar³ = 0.15625

The first four terms are 10, 2.5 ,0.625, 0.15625

We know that

The sum of the first n terms of the GP

Sn = a[(1-r^n)/(1-r)]

Now ,

The sum of first 17 terms of the GP

=> S 17 = 10[(1-0.25¹⁷)/(1-0.25)]

=> S 17 = 10 [ (1-0.25¹⁷)/(0.75)]

=> S 17 = (10/0.75)(1-0.25¹⁷)

=> S 17 = (10/(75/100)(1-0.25¹⁷)

=> S 17 = (1000/75)(1-0.25¹⁷)

=> S 17 = (40/3)(1-0.25¹⁷)

=> S 17 = (40/3)[1-(25/100)¹⁷]

=> S 17 = (40/3)[1-(1/4)¹⁷]

=> S 17 = (40/3) [ 1-(1/17179869184)]

=> S 17 = (40/3) [ (17179869184-1)/17179869184]

=> S 17 = (40/3)(17179869183/17179869184)

=> S 17 = (40/3)(0.999999999417)

=> S 17 = (40×0.999999999417)/3

=> S 17 = 39.999999997671/3

=> S 17 = 13.333333332557

=> S 17 = 13.3 (Round it to 1 decimal)

Answer:-

i) The first four terms of the given GP = 10, 2.5 , 0.625 , 0.15625

ii) The Sum of first 17 terms of the GP = 13.3

Used formulae:-

• The general form of a GP is a ,ar,ar²,ar³,...

• The sum of the first n terms of the GP
• Sn = a[(1-r^n)/(1-r)]