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

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