Clara's class is going on a trip to the local science museum. Twenty-five students, one teacher, and three parents are going on
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Given:
The first two terms in an arithmetic progression are -2 and 5.
The last term in the progression is the only number in the progression that is greater than 200.
To find:
The sum of all the terms in the progression.
Solution:
We have,
First term :
Common difference :
nth term of an A.P. is
where, a is first term and d is common difference.
According to the equation, .
Divide both sides by 7.
Add 1 on both sides.
So, least possible integer value is 30. It means, A.P. has 30 term.
Sum of n terms of an A.P. is
Substituting n=30, a=-2 and d=7, we get
Therefore, the sum of all the terms in the progression is 2985.