# Find the sum of the terms in the arithmetic sequence below, {eq}S_n {/eq}. {eq}7, 4, 1, -2, ..., -47 {/eq}

## Question:

Find the sum of the terms in the arithmetic sequence below, {eq}S_n {/eq}.

{eq}7, 4, 1, -2, ..., -47 {/eq}

## Arithmetic Sequence:

In mathematics, an arithmetic sequence is a list of number that is arranged in a way such that the difference between two consecutive numbers is always same or constant.

The {eq}{n^{th}} {/eq} or the last term {eq}(l) {/eq} of an arithmetic sequence is:

{eq}l = a + (n - 1)d {/eq}

The sum {eq}({S_n}) {/eq} of the terms in an arithmetic sequence is:

{eq}{S_n} = \dfrac{n}{2}(a + l) {/eq}

Here,

• The first term is {eq}a {/eq}.
• The last term is {eq}l {/eq}.
• The total number of terms is {eq}n {/eq}.
• The common difference between two terms is {eq}d {/eq}.

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Given Data:

The given arithmetic sequence is: {eq}7,\;4,\;1,\; - 2,\;......, - 47 {/eq}.

For the given sequence,

{eq}a = 7,\;d = 4 - 7 = -...