The sum of terms of the AP 34 + 32 + 30 + .... + 10 is
The formula to find the nth term of an arithmetic progression is tn=a+(n−1)d
Where,
'a1' is the first term,
'd' is the common difference,
'n' is the no. of terms,
'tn' is the nth term.
Here,
a1 = 34
a2 = 32
d = a2 - a1 = 32 - 34 = -2
tn = 10
Substituting the given values in the equation to find the nth term, we get
10=34+(n−1)(−2)
(n−1)(−2)=−24
n−1=242=12
⇒ n=13
Sum of n terms of an AP is given by,
Sn=n2 (first term + last term)
S13=132(34+10)
⇒ S13=286