Problem

Find the sum of the first 30 terms of the sequence. $3,12,21,30, \ldots$ \[ S_{30}= \]

Solution

Step 1 :We are given an arithmetic sequence where the common difference is 9 (12-3 = 9, 21-12 = 9, 30-21 = 9).

Step 2 :The sum of the first n terms of an arithmetic sequence can be found using the formula: \(S_n = \frac{n}{2} * (a_1 + a_n)\) where n is the number of terms, a_1 is the first term, and a_n is the nth term.

Step 3 :In this case, n = 30, a_1 = 3, and a_n = a_1 + (n-1)*d = 3 + (30-1)*9 = 267.

Step 4 :We can substitute these values into the formula to find the sum of the first 30 terms.

Step 5 :n = 30, a_1 = 3, d = 9, a_n = 264, S_n = 4005.0

Step 6 :The sum of the first 30 terms of the sequence is \(\boxed{4005}\).

From Solvely APP
Source: https://solvelyapp.com/problems/16742/

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