Question

If the first term and common difference of an arithmetic
sequence are equal, find the relation between 5th term
and 10th term?
​

Answer 1

$Let \: 'a' \: and \: 'd' \: are \: first \: term\:and$

$Common \: difference \: of \: an \: A.P$

$Given \: a = d \: --(1)$

$We \: know \: that ,$

$\boxed{\pink{ n^{th}\: term (a_{n} = a + (n-1)d }}$

$i) 5^{th} \:term = a + (5-1)d$

$\implies a_{5} = a + 4d$

$\implies a_{5} = a + 4a = \blue { 5a } \: --(2)$

$ii) 10^{th} \:term = a + (10-1)d$

$\implies a_{10} = a + 9d$

$\implies a_{10} = a + 9a$

$= 10a$

$= 2 \times (5a)$

$= 2\pink{ a_{5}}$

Therefore.,

$\red{ 10^{th} \:term} \green { \:is \: twice \: the }$

$\green { 5^{th} \:term}$

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