# If the 6th term of an arithmetic sequence is 48 and the sum of the first 6 term is 300, what is...

## Question:

If the {eq}6 {/eq} th term of an arithmetic sequence is {eq}48 {/eq} and the sum of the first {eq}6 {/eq} term is {eq}300 {/eq}, what is the first term and the constant difference?

## Arithmetic Progression

Arithmetic Progression (A.P.) is a sequence of numbers that have a constant difference between two successive terms.

This constant difference is known as the common difference (d).

Let's consider an A.P.

{eq}\displaystyle a,a + d,a + 2d,............a + (n-1)d....... {/eq}

Here {eq}null{/eq}

and the common difference {eq}{/eq}

#### nth term of an A.P.

{eq}\displaystyle T_{n} = a_{n} = a + (n-1)d {/eq}

#### Sum of 'n' terms of an A.P.

{eq}\displaystyle S_{n} = \frac{n}{2} (a + a_{n}) = \frac{n}{2} (2a + (n-1)d) {/eq}

## Answer and Explanation: 1

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The 6th term of an arithmetic sequence is 48, it means

{eq}\displaystyle a_{n} = a + (n-1)d {/eq}

{eq}\displaystyle a_{6} = a + (6-1)d = a...

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Chapter 26 / Lesson 8An arithmetic series is the sum of a sequence in which each term is computed from the previous one by adding (or subtracting) a constant. Discover the equations and formulas in an arithmetic series.