Question

6. Write the AP when the first term 'a' and the CD'd' is given as a = 4
and d =3
​

Answer 1

$\huge\underline{\bf{Given}}$

• First term (a) = 4
• Common difference (d) = 3

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$\huge\underline{\bf{To\: find}}$

• The required A.P.

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$\huge\underline{\bf{Solution}}$

• We have given first term and the common difference and now we wish to calculate the 2nd, 3rd and 4th term.

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★ Formula used

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

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$\sf\pink{Second\: term}$

$\tt\longmapsto{a_2 = 4 + (2 - 1)3}$

$\tt\longmapsto{a_2 = 4 + (1)3}$

$\tt\longmapsto{a_2 = 4 + 3}$

$\tt\longmapsto{a_2 = 7}$

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$\sf\pink{Third\: term}$

$\tt\longmapsto{a_3 = 4 + (3 - 1)3}$

$\tt\longmapsto{a_3 = 4 + (2)3}$

$\tt\longmapsto{a_3 = 4 + 6}$

$\tt\longmapsto{a_3 = 10}$

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$\sf\pink{Fourth\: term}$

$\tt\longmapsto{a_4 = 4 + (4 - 1)3}$

$\tt\longmapsto{a_4 = 4 + (3)3}$

$\tt\longmapsto{a_4 = 4 + 9}$

$\tt\longmapsto{a_4 = 13}$

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Hence, required A.P.

$\: \: \: \: \: \: \: \: \: \: \: \boxed{\bf{\bigstar{A.P. = a, a_2, a_3, a_4......a_n{\bigstar}}}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {A.P. = 4, 7, 10, 13....}$

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Answer 2

Question :-

Write the AP when the first term 'a' and the CD'd' is given as a = 4

and d =3

Answer :-

{ A.P. = 4, 7, 10, 13 , 16 }

Given :-

a = 4

d = 3

Here ,

" a " = First term of an A.P

" d " = Common difference of an A.P

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Have to Find :-

Write the A.P.

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Calculations :-

As we all know the formula of finding an A.P .

Let's simply apply the formula here :-

$\large{\boxed{\bold{a_n\:=\:a + (n - 1)d}}}$

aₙ=a+(n-1)d

• Second term

↠ a_2 = 4 + (2 - 1) 3

↠ a_2 = 4 + 1 × 3

↠ a_2 = 4 + 3

↠ a_2 = 7

• Third term

↠ a_3 = 4 + ( 3 - 1 ) × 3

↠ a_3 = 4 + 2 × 3

↠ a_3 = 4 + 6

↠ a_3 = 10

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• Fourth term

↠ a_4 = 4 + ( 4 - 1 ) × 3

↠ a_4 = 4 + 3 × 3

↠ a_4 = 4 + 9

↠ a_4 = 13

• Fifth term

↠ a_5 = 4 + ( 5 - 1 ) × 3

↠ a_5 = 4 + 4 × 3

↠ a_5 = 4 + 12

↠ a_5 = 16

A.P. = 4, 7, 10, 13 , 16 .....