# If the third term in an arithmetic sequence is 7 and the common difference is -5, what is the...

## Question:

If the third term in an arithmetic sequence is 7 and the common difference is -5, what is the value of the fourth term?

## Arithmetic sequence:-

In mathematics, a succession of numbers is said to be an arithmetic sequence if the difference between any two consecutive terms and the preceding it is constant throughout.

This constant is called a common difference in that arithmetic sequence.

the nth term of an arithmetic progression or arithmetic sequence:-

Let 'a' be the first term and 'd' is a common difference of an A. P. So the nth term of A. P. is given by the following formula:-

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

and the sum of an A. P. is given by the following formula:-

{eq}S_n = \frac{n}{2} [2a+(n-1)d] {/eq}

where 'a' is the first term and 'd' is the common difference of A. P.

Working rule:-

if the terms of a sequence are given to be {eq}t_1, t_2, t_3, ....... {/eq}

they will be in A. P.

if {eq}t_2- t_1 = t_3- t_2=t_4- t_3=........=d {/eq}

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Given:-

{eq}a_3= 7 {/eq}

d = -5

find{eq}a_4=? {/eq}

so we have {eq}a_4 - a_3 = d {/eq}

{eq}\displaystyle \Rightarrow a_4 - 7=-5 {/eq}

{eq}\d...