Question

The second term of the ap is 13 and 5th term is 25,then 7th term is​​

Answer 1

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$\huge\sf\red{Given\::}$

$\leadsto\:\sf a_{2} = a + d$

$\leadsto\:\sf a_{5} = a + 4d$

$\leadsto\:\sf a + d = 13$_______①

$\leadsto\:\sf a + 4d = 25$_______②

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$\huge\sf\pink{Solution\::}$

$\sf\orange{From\: equation\:(1)\:\&\:(2)\::}$

$\implies\sf a + 4d = 25$

$\implies\sf a + d = 13$

$\implies\sf 3d = 12$

$\implies\sf d =\dfrac{\cancel{12}}{\cancel{3}}$

$\implies\sf d\:=\;4$

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$\small\sf\purple{Substituting\:x\: value\:in\; Equation\;(1)}$

$\longrightarrow\:\sf a + d = 13$

$\longrightarrow\:\sf a + 4 = 13$

$\longrightarrow\:\sf a = 13 - 4$

$\longrightarrow\:\sf a = 9$

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$\small\sf\blue{Finding\: 7^{th}\: Term}$

$\dashrightarrow\:\sf a_{7} = a + 6d$

$\dashrightarrow\:\sf a_{7} = a + 6(4)$

$\dashrightarrow\:\sf a_{7} = 9 + 24$

$\dashrightarrow\:\sf a_{7} \:=\: 33$

$\small\bold{\underline{\boxed{\sf{\green{Hence,\:7th\;Term\:of\;the\;Given\;AP\;is \;33.}}}}}$

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Answer 2

Answer:

acc. to question

a+d = 13

a+4d = 25..

then by solving it..

d=4 ( a+ d=13)

a=9 (a+4d=25) a cancle with a..... d-4d = -3d... 13-25=-12

therefore - and - sign cancel.. therefore d= 12/3=4

after getting valur of d we can easily find value if a...... after getting both the value we can find the 7th term.. by a+6d=9+6*4 = 33..

answer = 33