SOLUTION: Consider the sequence of numbers : 2;5;2;9;2;13;2;17;..... Calculate the sum of the first 100 terms of the sequence Please help me I begg.

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Question 1140444: Consider the sequence of numbers : 2;5;2;9;2;13;2;17;.....
Calculate the sum of the first 100 terms of the sequence
Please help me I begg.

Found 2 solutions by Boreal, MathTherapy:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
There will be 50 terms of 2 (sum is 100)
the other 50 terms are an arithmetic series of 5+9+13+17..., and there are 50 of them with a difference between each of 4.
The sum is S50=(n/2)(a1+an), n=50
an=a1+d(n-1)=5+4(49)=201
so the sum S50=25(5+201)=25(506)=12650
so the total sum is 12,750

Answer by MathTherapy(10557)   (Show Source): You can put this solution on YOUR website!
Consider the sequence of numbers : 2;5;2;9;2;13;2;17;.....
Calculate the sum of the first 100 terms of the sequence
Please help me I begg.
2 is the ODD term in the sequence, and since there are 50 of them, the sum of the ODD terms (Terms 1,3,5,7,9, etc.) is 100 (50 * 2)
The EVEN terms (Terms 2,4,6,8,10, etc.) starts with 5 and since there are 50 of them, we use the following formula for the sum of an AP:
------ Substituting 50 for n (number of terms), , and 4 for d (common difference)

Sum of 1st 100 terms of sequence:
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