The 10th, 4th and 1st term of an A. P are three consecutive find the common ratio of the G. P and the sum of the 6th term, taking the 1st term to be 4

S_6 = 252

Step-by-step explanation:

We are told that the 10th, 4th and 1st term of an A.P are three consecutive terms of a G.P.

Now,formula for nth term of an AP is;

a_n = a + (n - 1)d

Thus;

a_10 = a + (10 - 1)d

a_10 = a + 9d

Also;

a_4 = a + (4 - 1)d

a_4 = a + 3d

First term is a.

Thus, since they are consecutive terms of a G.P, it means that;

(a + 9d)/(a + 3d) = (a + 3d)/a

Cross multiply to get;

a(a + 9d) = (a + 3d)(a + 3d)

a² + 9ad = a² + 6ad + 9d²

a² will cancel out to give;

9ad - 6ad = 9d²

3ad = 9d²

Divide both sides by 3d to get;

a = 3d

We are told that the first term is 4.

Thus, 4 = 3d

d = 4/3

We saw earlier that ratio of the GP is (a + 3d)/a

Thus; r = (4 + 3(4/3))/4 = 8/4 = 2

Sum of n terms of a G.P is given by;

S_n = a(rⁿ - 1)/(r - 1)

S_6 = 4(2^(6) - 1)/(2 - 1)

S_6 = 252

3x + 18 = 147°

step-by-step explanation:

3x + 18 = 147°, because the value of the central angle is equal to the value of the arc formed by it.

i hope i you.

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have