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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 =S
n
=400
S
n
=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.
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