Question

If the first term of a sequence is 5 and the tenth term is -58, what is the common difference? -3 -4 -5 -6 -7

Answer 1

Common difference of the sequence is -7.

Explanation:

Given:

First term a = 5

Tenth term
`T_(10)` = -58

we need to find the common difference d.

Now let the number of terms will be 10 since tenth term is given;

Hence n =10

Now Using Arithmetic Progression formula we get;

`T_n = a+(n-1)d`

Now Substituting the given values in the formula we get;

`T_(10)=5+(10-1)d\\-58 = 5+9d\\-58-5=9d\\-63=9d\\\\-(63)/(9)=d\\\\d=-7`

Hence Common difference of the sequence will be -7.