Question

9th term is equal to 6 times of 2nd term of an A.P & 5th term of an a.p is 22 find the A.P

Answer 1

your answer is 2 ,7 ,12 ,.... where a=2 ,d=5

Answer 2

Answers:

$\huge{\boxed{\boxed{\sf{A.P=2,7,12,17.....}}}}$

Step-by-step explanation:

$\huge{\boxed{\boxed{\underline{\sf{SOLUTION-}}}}}$

□a9=6(a2)

□a5=22

○A.P=?

>>According to the question:

$a9 = 6(a2) \\ a + 8d = 6(a + d) \\ a + 8d = 6a + 6d \\ a - 6a + 8d - 6d = 0 \\ 2d - 5a = 0 - - - - - (1) \\ \\ a5 = 22 \\ a + 4d = 22 - - - - - ( 2) \\ \\ multiplying \: 2 \: in \: (1) \: and \: 1 \: in \: (2) \\ 4d - 10a = 0 - - - - - (3) \\ a + 4d = 22 - - - - - (4) \\ subtracting \:( 4) \: from \: (3) \\ 4d - 10a - a - 4d = 0 - 22 \\ - 11a = - 22 \\ a = \frac{ - 22}{ - 11} \\ a = 2 \\ \\putting \: value \: of \: a \: in \: (3) \\ 4d - 10 \times 2 = 0 \\ 4d = 20 \\ d = \frac{20}{4} \\ d = 5$

$\huge{\boxed{\boxed{\sf{A.P=2,7,12,17.....}}}}$

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