Question

What is the common difference of AP whose first term is 1/6 and 6th term is is 3.5?​

Answer 1

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Q) What is the common difference of AP whose first term is $\dfrac{1}{6}$and 6th term is 3.5 .

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☆ Given :

• It's an A.P.
• First term = a = $\dfrac{1}{6}$
• 6th term = $\sf a_6$ = 3.5

☆ To Find :

• Common Difference = ?

☆ Solution :

Since , we have

• a = $\dfrac{1}{6}$

Using the Formula for n th term

$\boxed{ \rm \: a _{n} = a + (n - 1)d}$

as we have the 6th term = 3.5 ,

put n = 6 ,

$\rm \mapsto \: 6th \: term = \frac{1}{6} + (6 - 1) \times d$

$\mapsto \rm \: 3.5 = \frac{1}{6} + 5d$

$\mapsto \rm \: 5d = 3.5 - \frac{1}{6}$

$\mapsto \rm \: 5d = \frac{21 - 1}{6}$

$\mapsto \rm \cancel5d = \frac{ \cancel{20}}{6}$

$\mapsto \rm \: d = \frac{ \cancel4}{ \cancel6}$

$\green \star \: \: \: \: \pink{\boxed{ \rm \: d = \frac{2}{3} }}$

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☆ Know More :

• An AP is a sequence in which adjacent terms differ with a common Difference .

$\sf \: a _{n} = a + (n - 1)d$

$\sf \: s _{n} = \frac{n}{2} \{2a + (n - 1)d \}$

$\sf \: s _{n} = \frac{n}{2} \{a + a _{n} \}$

Where ,

$\pink{ \ddot{ \smile}} \: \rm \: a = first \: term \:$

$\purple{ \ddot{ \smile}} \: \: \rm \: d = common \: difference$

$\green{ \ddot{ \smile}} \: \: \: \rm n = no. \: of \: terms$

$\red{ \ddot{ \smile}} \: \: \rm \: a _{n} = {n}^{th} \: term$

$\orange{ \ddot{ \smile}} \: \: \rm \: s_{n} = sum \: of \: n \: terms$