Question

Fill in the blanks with next ters of a A.P.
1) 5, 8, 11, 14.
2) 2, 9, 16.
3) -1,-5,-9.​

Answer 1

1. 5, 8, 11, 14, _, _, _

a = 5

f = 8-5 => 3

Next terms :

14 + 3 = 17

17 + 3 = 20

20 + 3 = 23

Next three terms of AP will be 17, 20, 23.

2. 2, 9, 16, _, _, _

a = 2

d = 9-2 => 7

16 + 7 = 23

23 + 7 = 30

30 + 7 = 37

Next three terms of AP will be 23, 30, 37.

3. -1, -5, -9, _, _, _

a = -1

d = -5 + 1=> -4

- 9 - 4 = -13

- 13 - 4 = - 17

- 17 - 4 = - 21

Next three terms of AP will be -13, -17, -21.

Answer 2

$\huge\bold{\green{\underbrace{\orange{QUESTION:-}}}}$

✍️ Fill in the blanks with next three terms of the following A.P .

1) 5, 8, 11, 14, _, _, _ .

2) 2, 9, 16, _, _, _ .

3) -1, -5, -9, _, _, _ .

_______________________________

FORMULA :-

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

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$\huge\bold{\green{\underbrace{\orange{SOLUTION:-}}}}$

1) 5, 8, 11, 14, _, _, _ .

✍️ Here,

• first term (a) = 5

• common difference (d) = (8 - 5) = 3 or (11 - 8) = 3 or (14 - 11) = 3

✍️ So, now we can calculate the 5th, 6th and 7th term of the A.P .

✍️ 5th term of the A.P is,

$\checkmark\:\rm{\red{a_5\:=\:a\:+\:(5\:-\:1)\:d}}$

$\rm{\implies\:a_5\:=\:a\:+\:4d\:}$

$\rm{\implies\:a_5\:=\:5\:+\:4\times{3}\:}$

$\rm{\purple{\boxed{\implies\:a_5\:=\:17\:}}}$

✍️ 6th term of the A.P is,

$\checkmark\:\rm{\red{a_6\:=\:a\:+\:(6\:-\:1)\:d}}$

$\rm{\implies\:a_6\:=\:5\:+\:5\times{3}\:}$

$\rm{\purple{\boxed{\implies\:a_6\:=\:20\:}}}$

✍️ 7th term of the A.P is,

$\checkmark\:\rm{\red{a_7\:=\:a\:+\:(7\:-\:1)\:d}}$

$\rm{\implies\:a_7\:=\:5\:+\:6\times{3}\:}$

$\rm{\purple{\boxed{\implies\:a_7\:=\:23\:}}}$

$\therefore\:\rm{\blue{5\:,\:8\:,\:11\:,\:14\:,\:{\bold{\underline{17\:,\:20\:,\:23\:}}}\:}}$

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2) 2, 9, 16, _, _, _ .

✍️ Here,

• first term (a) = 2

• common difference (d) = (9 - 2) = 7 or (16 - 9) = 7

✍️ So, now we can calculate the 4th, 5th and 6th term of the A.P .

✍️ 4th term of the A.P is,

$\checkmark\:\rm{\red{a_4\:=\:a\:+\:(4\:-\:1)\:d}}$

$\rm{\implies\:a_4\:=\:2\:+\:3\times{7}\:}$

$\rm{\purple{\boxed{\implies\:a_4\:=\:23\:}}}$

✍️ 5th term of the A.P is,

$\checkmark\:\rm{\red{a_5\:=\:a\:+\:(5\:-\:1)\:d}}$

$\rm{\implies\:a_5\:=\:2\:+\:4\times{7}\:}$

$\rm{\purple{\boxed{\implies\:a_5\:=\:30\:}}}$

✍️ 6th term of the A.P is,

$\checkmark\:\rm{\red{a_6\:=\:a\:+\:(6\:-\:1)\:d}}$

$\rm{\implies\:a_6\:=\:2\:+\:5\times{7}\:}$

$\rm{\purple{\boxed{\implies\:a_6\:=\:37\:}}}$

$\therefore\:\rm{\blue{2\:,\:9\:,\:11\:,\:{\bold{\underline{23\:,\:30\:,\:37}}}\:}}$

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3) -1, -5, -9, _, _, _ .

✍️ Here,

• first term (a) = -1

• common difference (d) = [-5 - (-1)] = (-5 + 1) = -4 or [-9 - (-5)] = (-9 + 5) = -4 .

✍️ So, now we can calculate the 4th, 5th and 6th term of the A.P .

✍️ 4th term of the A.P is,

$\checkmark\:\rm{\red{a_4\:=\:a\:+\:(4\:-\:1)\:d}}$

$\rm{\implies\:a_4\:=\:-1\:+\:3\times{-4}\:}$

$\rm{\purple{\boxed{\implies\:a_4\:=\:-13\:}}}$

✍️ 5th term of the A.P is,

$\checkmark\:\rm{\red{a_5\:=\:a\:+\:(5\:-\:1)\:d\:}}$

$\rm{\implies\:a_5\:=\:-1\:+\:4\times{-4}\:}$

$\rm{\purple{\boxed{\implies\:a_5\:=\:-17\:}}}$

✍️ 6th term of the A.P is,

$\checkmark\:\rm{\red{a_6\:=\:a\:+\:(6\:-\:1)\:d\:}}$

$\rm{\implies\:a_6\:=\:-1\:+\:5\times{-4}\:}$

$\rm{\purple{\boxed{\implies\:a_6\:=\:-21\:}}}$

$\therefore\:\rm{\blue{-1\:,\:-5\:,\:-9\:,\:{\bold{\underline{-13\:,\:-17\:,\:-21\:}}}\:}}$

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