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