Question

2) Find the common difference in the arithmetic sequence, an, in which a1 = 16 and a9 = 36.
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Answer 1

The common difference in the arithmetic sequence is 2.5

What is arithmetic sequence ?

Arithmetic sequence is a sequence in which the differences between consecutive terms are always same.

Example : 2, 5, 8, 11, ..... is an arithmetic sequence where the common difference is 3.

What is the formula of arithmetic sequence ?

Formula of arithmetic sequence is $a_{n} =a_{1}+(n-1)d$ ,

where $a_{n}$= $n^{th}$ term in the sequence,

$a_{1}$= $1^{st}$ term in the sequence,

d = common difference between terms

How to find required common difference ?

Given, $a_{1}$ = 16 and $a_{9}$ = 36

Let, d be the common difference.

∴ From the formula of arithmetic sequence,

   $a_{9} =a_{1}+(9-1)d$

⇒ 36 = 16+8d

⇒ 36-16=8d

⇒ 20=8d

⇒ d = 20/8

⇒ d = 5/2 = 2.5

Hence, The common difference is 2.5

Learn more about arithmetic sequence here :

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