Arithmetic Series
First three terms are 17,26 and 35
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