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