I need to find the sum of the terms of the series 4+7+10+.....+22

genestesya
2022-09-14
Answered

I need to find the sum of the terms of the series 4+7+10+.....+22

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Karla Bautista

Answered 2022-09-15
Author has **16** answers

It is the sum of an arithmetic progression (series) with first term

${a}_{1}=4$ and ratio r=3

The sum is

${S}_{7}=\frac{7}{2}\cdot ({a}_{1}+{a}_{7})=\frac{7}{2}\cdot (4+22)=7\cdot 13=91$

${a}_{1}=4$ and ratio r=3

The sum is

${S}_{7}=\frac{7}{2}\cdot ({a}_{1}+{a}_{7})=\frac{7}{2}\cdot (4+22)=7\cdot 13=91$

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We have the sequence $\{0,1,2,3,3,4,6,9,8,\dots \}$ for which we have to find the summation of terms to the nth term, $C}_{n$

However, the number of terms in the sub sequence,$N\ne n$ , the number of terms in the larger sequence. What is a way to represent N in terms of n in order to arrive at a single formula for $C}_{n$ ? I've determined that it can be $N=\frac{n}{3}$ but this is only true for cases where n is a multiple of 3. How do I find those two cases where n isn't a multiple of 3?

However, the number of terms in the sub sequence,