Question

4 Pierre starts counting at 88 and counts back in steps of 8. 88, 80, 72, 64, ... Will the number 1 be in the sequence? How can you tell without counting back? 5 Sofia male​

Answer 1

Answer:

$\boxed{\sf \: \bf \: 1 \: is \: not \: the \: number \:in \: sequence \: of \: \: 88,80,72,... \: }$

Step-by-step explanation:

Given that, Pierre starts counting at 88 and counts back in steps of 8 as 88, 80, 72, 64, ...

Now, we have to check whether 1 will be in the sequence or not.

The given sequence is 88, 80, 72, 64, ...

So, we have First term, a = 88

Common difference, d = 80 - 88 = - 8

Let assume that $\sf \: n^{th}$ term of an AP be 1

Wᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

↝ nᵗʰ term of an arithmetic sequence is,

$\begin{gathered}\bigstar\:\:{\underline{{\boxed{\bf{{a_n\:=\:a\:+\:(n\:-\:1)\:d}}}}}} \\ \end{gathered}$

Wʜᴇʀᴇ,

a is the first term of the sequence.

n is the no. of terms.

d is the common difference.

So, on substituting the values in above formula, we get

$\sf \: 88 + (n - 1)( - 8) = 1$

$\sf \: 88 - 8n + 8 = 1$

$\sf \: 96 - 8n = 1$

$\sf \: - 8n = 1 - 96$

$\sf \: - 8n = - 95$

$\sf \: 8n = 95$

$\implies\sf \: n = \dfrac{95}{8} \: \cancel{\in} \: Integer$

Hence,

$\implies\boxed{\sf \: \bf \: 1 \: is \: not \: the \: term \: of \: 88,80,72,... \: }$