Arithmetic Series
The first three terms are 17, 26 and 35
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