Question

The first term of an arithmetic sequence is -3 and thefifth term is 53 what is the common difference of the sequence

Answer 1

In an arithmetic sequence, you start from the first element, and then you generate the next one by adding a common difference.

So, let's say you start from $x$ and add a common difference of $d$. The first elements are

$a_1=x$

$a_2=x+d$

$a_3=(x+d)+d=x+2d$

$a_4=(x+2d)+d=x+3d$

$a_5=(x+3d)+d=x+4d$

Since we know that $a_5 = 53$, and $x = -3$, we can solve for $d$:

$a_5 = x+4d \iff 53 = -3+4d \iff 56 = 4d \iff d = \dfrac{56}{4} = 14$

So, the common difference is 14