Question

Write the next two terms of A. P. if a = 10 & d = 2.​

Answer 1

Answer:

a = t1 = 10 - given

d = 2. - given

We know that,

t2 = a + d

= 10 + 2

:. t2 = 12

t3 = a + 2d. OR t3 = t2 + d

= 10 + 2(2) t3 = 12 + 2

= 10 + 4. :. t3 = 14

:. t3 = 14

:. the next two terms are 12 and 14.

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Answer 2

Given :

• a or First Term of A.P is 10 .
• d or Common Difference is 2 .

Need To Find :

The next two term of an A.P are -:

• $a_{2}$ Second term of an A.P .
• $a_{3}$ Third term of an A.P .

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❍ Finding $a_{2}$ of A.P :

$\dag\frak{\underline { As,\:We\:know\:that\::}}$

$\underline {\boxed { \sf { \star a_{n} = a + ( n - 1) d}}}$

Where ,

• n is the number of terms , d is common Difference & a is the first term of A.P .

Then ,

$\underline {\boxed { \sf { \star a_{2} = a + ( 2 - 1) d}}}$

$\underline {\frak{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$:\implies \sf{ a_{2} = 10 + (2-1) 2 }$

$:\implies \sf{ a_{2} = 10 + (1) 2 }$

$:\implies \sf{ a_{2} = 10 + 2 }$

$\underline {\boxed{\pink{ \mathrm {  a_{2}\:or\:Second \:Term\:= 12\: }}}}\:\bf{\bigstar}$

And ,

$\underline {\boxed { \sf { \star a_{3} = a + ( 3 - 1) d}}}$

$\underline {\frak{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$:\implies \sf{ a_{3} = 10 + (3-1) 2 }$

$:\implies \sf{ a_{3} = 10 + (2) 2 }$

$:\implies \sf{ a_{3} = 10 + 4 }$

$\underline {\boxed{\pink{ \mathrm {  a_{3}\:or\:Third \:Term\:= 14\: }}}}\:\bf{\bigstar}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Hence,\:The\:next\:two\:term\:of\:an\:A.P\:are\:\bf{12\:and\:14}.}}}$

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