the second term of an ap is 15 and the fifth term ids double the first find the first term of an ap and the common difference of this ap

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Solution

Let a = first term ; d = common difference
Second term, a₂= a + d = 15 ..........(1)
also, a₅= 2 (a)
$\Rightarrow$ a + 4d = 2a
$\Rightarrow$ a = 4d ............(2)
put a = 4d in (1), we get
4d + d = 15
$\Rightarrow$ 5d = 15 $\Rightarrow d = 3$
from (2), we get a = 12

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the second term of an ap is 15 and the fifth term ids double the first find the first term of an ap and the common difference of this ap

Let a = first term ; d = common differenceSecond term, a2 = a + d = 15 ..........(1)also, a5 = 2 (a) ⇒a + 4d = 2a ⇒a = 4d ............(2) put a = 4d in (1), we get4d + d = 15⇒5d = 15 ⇒d = 3from (2), we get a = 12

Let a = first term ; d = common difference
Second term, a₂= a + d = 15 ..........(1)
also, a₅= 2 (a)
$\Rightarrow$ a + 4d = 2a
$\Rightarrow$ a = 4d ............(2)
put a = 4d in (1), we get
4d + d = 15
$\Rightarrow$ 5d = 15 $\Rightarrow d = 3$
from (2), we get a = 12