In the given question it is asked to calculate the common difference, if the first term is -4, the last term is 29 and the sum of all the terms is 150 of an AP.
Book RS Aggarwal, Class 10, chapter 5C, question no 22.
Rajan@2021Guru
In an AP, the first term is -4, the last term is 29 and the sum of all the terms is 150. Find its common difference.
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Let d be the common difference.
Given:
First term =a=−4
Last term =l=29
Sum of all the terms =Sn=150
Sn=n/2[a+l]
150=n/2[−4+29]
n=12
There are 12 terms in total.
Therefore, 29 is the 12th term of the AP.
Now, 29=−4+(12−1)d
29=−4+11d
d=3
The common difference is 3.