An important and exam oriented question from arithmetic progression chapter as it was already asked in previous year paper of 2012, 2014, 2017 in which we are to find the common difference and the no of terms, if the first and last term of an AP are 5 and 45 respectively their sum of all its terms is 400.
Book RS Aggarwal, Class 10, chapter 5C, question no 24.
Let n be the total number of terms and d be the common difference.
Given:
First term=a=5
Last term =l=45
Sum of all terms =Sn=400
Sn=n/2[a+l]
400=n/2[5+45]
n/2=400/50
n=16
There are 16 terms in the AP.
Therefore, 45 is the 16th term of the AP.
45=a+(16−1)d
45=5+15d
40=15d
15d=40
d=8/3
Common difference =d=8/3
Common difference is 8/3 and the number of terms are 16.