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

1.	The second term of the ap is 13 and 5th term is 25,then 7th term is
Answer» $\rule{250}3$ $\huge\sf\red{Given\::}$ $\leadsto\:\sf a_{2} = a + d$ $\leadsto\:\sf a_{5} = a + 4d$ $\leadsto\:\sf a + d = 13$ _______① $\leadsto\:\sf a + 4d = 25$ _______② $\rule{250}3$ $\huge\sf\pink{Solution\::}$ $\sf\orange{From\: equation\:(1)\:\&\:(2)\::}$ $\implies\sf a + 4d = 25$ $\implies\sf a + d = 13$ $\implies\sf 3d = 12$ $\implies\sf d =\dfrac{\cancel{12}}{\cancel{3}}$ $\implies\sf d\:=\;4$ $\rule{150}2$ $\small\sf\purple{Substituting\:x\: value\:in\; Equation\;(1)}$ $\longrightarrow\:\sf a + d = 13$ $\longrightarrow\:\sf a + 4 = 13$ $\longrightarrow\:\sf a = 13 - 4$ $\longrightarrow\:\sf a = 9$ $\rule{150}2$ $\small\sf\blue{Finding\: 7^{th}\: Term}$ $\dashrightarrow\:\sf a_{7} = a + 6d$ $\dashrightarrow\:\sf a_{7} = a + 6(4)$ $\dashrightarrow\:\sf a_{7} = 9 + 24$ $\dashrightarrow\:\sf a_{7} \:=\: 33$ $\small\bold{\underline{\boxed{\sf{\green{Hence,\:7th\;Term\:of\;the\;Given\;AP\;is \;33.}}}}}$ $\rule{250}3$

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