Find the sum of first 20 terms of the arithmetic series in which 3rd term is 7 and 7th term is 2 more than three times its 3rd term.

740

Step-by-step explanation:

Let the AP be a, a+d, a+2d, a+3d, ...

The  term of AP is given by:

We are given that the third term is 7.

⇒  

⇒

Also, the seventh term is 2 more than three times the third term.

⇒

⇒

⇒

⇒

⇒

We can put it in (1)

⇒

⇒

⇒d=4

Now, the Sum of n terms of an AP is given by the formula:

So, Sum of first 20 terms would be:

⇒

⇒

⇒

⇒

Thus, The Sum of first 20 terms of the AP is 740.

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

read more on -

step-by-step explanation:

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.