Find the first 3 terms of the arithmetic series given aq=17, an=197, Sn=2247.
(*Hint: you may have to use both formulas)

Arithmetic Series

The first three terms are 17, 26 and 35

Step-by-step explanation:

Let the common difference of this Arithmetic Series = b

Given that nth term  of the Arithmetic Series an = 197

The sum of the Arithmetic Series Sn = 2247

1st term of the arithmetic progression is aq=17

The nth term of the arithmetic progression is  an= a + (n-1)b=197 ,

And total number of terms in Arithmetic Series is n.

The sum  of an  AP is  Sn is defined as

 Sn = (n/2) × (2a +(n-1) × b)

⇒ Sn = (n/2) × ( a+ a+(n-1) × b)

⇒ 2247 = (n/2) ×  (17 + 197)

⇒ 2247 = (n/2) × ( 214)

⇒ n/2 = 2247/(214)

 ⇒ n = 2247 ×  2 / 214

⇒ n = 21

Also, we know that

an = aq + (n-1) ×  b

⇒ 197=17 + (21-1) ×  b

⇒   197-17 = 20 *b

⇒  180/20 = b

⇒  b = 9

So the first three terms of the arithmetic progression are as follows

The first term, A1 = 17

The second term, A2 = a1 + b

                                 = 17 + 9

                                 = 26

The third term , A3 = a2+b

                                   =26 + 9

                                   =35

Hence the first three terms are 17, 26 and 35

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

positive

step-by-step explanation:

the quadrant is facing upwards