Find the first 3 terms of the arithmetic series given aq=17, an=197, Sn=2247.

(*Hint: you may have to use both formulas)

A

Arithmetic Series

First three terms are 17,26 and 35

Step-by-step explanation:

Let the common difference of this AP be b

Given 1st term of the arithmetic series is a1=17,

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

The sum of the Arithmetic progression is Sn = 2247

And total number of terms is n.

And we know that the formula of sum of an AP is

S = (n/2) * (2*a + (n-1) * b)

⇒ S = (n/2) * (a + a + (n-1) * b)

⇒2247 = (n/2) * (17 + 197)

therefore, n/2 = 2247 / (214) = 21

and hence the value of n from the equation is 21

and we also know that

an = a + (n-1) * b

⇒ 197=17 + (21-1) * b

⇒ 197-17 = 20 * b

⇒ 180/20 = b

And thus the value of b is 9

So the first three terms of the arithmetic progression is

The first term, A1 = 17

The second term, A2 = a1 + b

= 17 + 9

= 26

The third term, A3 = a2+b

=26 + 9

=35

Hence First three terms are 17,26 and 35