My approach.
You can see that the question mentions that it is A.P.You can also see that Common difference =-3
To find which term =-4
Let's assume -4 is the last term
First term =23 [first term]
The formula for no of terms = (First term- Last term)/distance between each term = (23+4)/3=9 [ distance is always +ve]
Now add 1 for -4 and 23 are both included in the sequence.No of terms =10
[ Think of this as "How many terms are there from 1 to 2? -> (First - second term)/distance bt each term = (2-1)/1 = 1.Since we know that both 1 and 2 are in the sequence,add 1 -> no of terms =2]
So if t(1)=23 then t(10) =-4
Hence answer =10
[This procedure saved me from tedious calculation]
if you wanna know the high school A.P forumula for no terms :
An = Ao + (n-1)d [ An is the nth term Ao is the first term d is the common difference n is the no of terms]
We know that:
Ao=23
An=-4
d=-3
-4 = 23 + (n-1)(-3)
-27= -3n+3
n=10
Therefore the n in An =-4 is 10
If you wanna know the high school formula for sum :
Sum = n/2 [2a+(n-1)d] [ n is the no of terms.a is the first term d is the common difference]
Also in an A.P avg = (First term value + last term value)/2 = Avg
If you know the no of terms, you can calculate sum directly from = Avg* no terms
