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Q.

For an AP with a first and last term as 2 and 29 respectively and the sum of all the terms as 155, the common difference is [[1]].


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answer is 3.

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Detailed Solution

For an AP with a first and last term as 2 and 29 respectively and the sum of all the terms as 155, the common difference is 3.
Given that the first and last term is 2 and 29. And the sum of all the terms is 155.
In the AP, the first term is 2, so,
a = 2.
And the last term is 29, so,
a n =1=29
where l is the last term.
The sum of all the terms is 155, so,
S n =155
The sum of the first n terms of an AP is found by using the formula,
S n = n 2 [a+l]
Substitute the known terms in the above formula.
155= n 2 (2+29) 155= n 2 (31)
Simplify the above equation to get the number of terms.
31n=155×2 31n=310 n=10
So the number of terms is 10.
The nth term can be found by using the formula,
a n =a+ n−1 d .
Substitute the known terms in the above formula,
29=2+(10−1)d
29−2=9d
9d=27 d=3
The common difference is 3.
 
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