# The sum of the first 20 terms of an arithmetic sequence with a common difference of 3 is 650....

## Question:

The sum of the first 20 terms of an arithmetic sequence with a common difference of 3 is 650. Find the first term.

## Arithmetic Sequence:

An important note about an arithmetic sequence is that the difference between each consecutive term (common difference) is the same, so if the common difference is not consistent, we can say with certainty that the progression is not arithmetic. If the value of the common difference is provided in the problem, then in order to find the sum of {eq}n {/eq} terms in a sequence, the following formula is quite advantageous:

$$S_n=\dfrac{n}{2}(2a_1+(n-1)d)$$

where:

• {eq}a_1 {/eq} is the first term.
• {eq}d {/eq} is a common difference.
• {eq}n {/eq} is the number of terms.

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Given Data:

• {eq}S_{20}=650 {/eq} is the sum of the first {eq}20 {/eq} terms.
• {eq}d=3 {/eq} is a common difference.
• {eq}n=20 {/eq} is the number...