Question

Consider the arithmetic sequence 6.10.14..
a) What is its common difference ?
b) What is its 10 term?
c) What is its algebraic form?​

Answer 1

$\rm\huge\blue{\underline{\underline{ Question : }}}$

Consider the arithmetic sequence 6,10,14..

a) What is its common difference ?

b) What is its 10 term?

c) What is its algebraic form?

$\rm\huge\blue{\underline{\underline{ Solution : }}}$

★ Given that,

• AP series : 6,10,14....

★ To find,

• (a) Common difference. (d)
• (b) 10th term.
• (c) Algebraic from.

★ Let,

(a) :-

• a1 = 6
• a2 = 10
• a3 = 14

$\tt\green{ : \implies Common \: difference (d) = a_{2} - a_{1} }$

$\sf\:\implies 10 - 6$

$\sf\:\implies 4$

Hence, the common difference (d) is " 4 ".

★ Now,

(b) :-

$\tt\green{ a_{10} = a + 9d }$

• a = 6
• d = 4

$\sf\:\implies a_{10} = 6 + 9(4)$

$\sf\:\implies a_{10} = 6 + 36$

$\sf\:\implies a_{10} = 42$

★ Finally,

(c) :-

Given AP series is : 6,10,14....

• a = 6
• d = 4

For natural numbers n,

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

• Substitute the values.

$\sf\:\implies a_{n} = 6 + (n - 1)4$

$\sf\:\implies a_{n} = 6 + 4n - 4$

$\sf\:\implies a_{n} = 2 + 4n$

Hence, algebraic form is 2 + 4n.

$\underline{\boxed{\bf{\purple{ \therefore Common\:diffference (d)= 4}}}}\:\orange{\bigstar}$

$\underline{\boxed{\bf{\purple{ \therefore 10^{th} term = 42}}}}\:\orange{\bigstar}$

$\underline{\boxed{\bf{\purple{ \therefore Algebraic\:form\:is \: 2 + 4n}}}}\:\orange{\bigstar}$

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★ Important formulas in AP :

$\rm\red{ :\implies a_{n} = a + (n - 1)d }$

$\rm\red{ :\implies S_{n} = \frac{n}{2} [ 2a + (n - 1)d ] }$

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Answer 2

Answer:

10-6=4

a+n-1xd

a=6

n=10

d=4

6+10-1x4

6+9x4

=

dn-f-d

4n+6-4

4n+2

Step-by-step explanation: