One of the most important and exam oriented question from arithmetic progression chapter as it was already asked in previous year paper of 2010 in which we are to find the common difference, if in an AP, the first term is 2, the last term is 29 and the sum of all the terms is 155.
Book RS Aggarwal, Class 10, chapter 5C, question no 21.
Let d be the common difference.
Given:
first term =a=2
last term =l=29
Sum of all the terms =Sn=155
Sn=n/2[a+l]
155=n/2[2+29]
n=10
There are 10 terms in total.
Therefore, 29 is the 10th term of the AP.
Now, 29=a+(10−1)d
29=2+2d
27=9d
d=3
The common difference is 3.