The first and last term of an arithmetic progression are 5 and 89 respectively.if the sun of de AP is 611 find de common difference?

Aliyuus2

1 year ago

Let n be the total number of terms and d be the common difference.
Given:
First term=a=5
Last term =l=89
Sum of all terms =Sn =611
Sn =n/2[a+l]
611=n/2[5+89]
n/2=611/94
n=6.5×2
n=13
There are 13 terms in the AP.
Therefore, 89 is the 13th term of the AP.
89=a+(13−1)d
89=5+12d
84=12d
12d=84
d=7
Common difference =d=7
Common difference is 7 and the number of terms are 13