Question

Consider the recursively defined sequence $a_n = a_{n-1} + \frac{5}{3}$, for $n \ge 1$ and with $a_0 = \frac{1}{5}$. Please find the sum of the first 37 terms by first finding an explicit formula for the terms of the sequence.

          Consider the recursively defined sequence $a_n = a_{n-1} + \frac{5}{3}$, for $n \ge 1$ and with $a_0 = \frac{1}{5}$.
Please find the sum of the first 37 terms by first finding an explicit formula for the terms of the sequence.

Consider the recursively defined sequence an = an-1 + (5)/(3), for n ≥ 1 and with a0 = (1)/(5).
Please find the sum of the first 37 terms by first finding an explicit formula for the terms of the sequence.

Added by Benjamin J.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert James Kiss

10/05/2022

Step 1

Step 1: We can write out the first few terms of the sequence to see if we can find a pattern: $a_0 = \frac{1}{5}$ $a_1 = a_0 + \frac{5}{3} = \frac{1}{5} + \frac{5}{3} = \frac{28}{15}$ $a_2 = a_1 + \frac{5}{3} = \frac{28}{15} + \frac{5}{3} = \frac{53}{15}$ $a_3 = Show more…

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Consider the recursively defined sequence $a_n = a_{n-1} + \frac{5}{3}$, for $n \ge 1$ and with $a_0 = \frac{1}{5}$. Please find the sum of the first 37 terms by first finding an explicit formula for the terms of the sequence.