Question

the 9th term of an ap is equal to 6times the second term .if its 5th term is 22 fond an ap

Answer 1

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✔️9th term of an AP = 6 * 2nd term

✔️a + ( 9 - 1 ) d = 6 ( a + ( 2 - 1 ) d

✔️a + 8d = 6 ( a + d)

✔️a + 8d = 6a + 6d

✔️8d - 6d = 6a - a

✔️2d = 5a

✔️d = 5/2 a

✔️Now its given tat 5th term is 22

✔️So,

✔️22 = a + (n-1)d

✔️22 = a + ( 5 - 1)d

✔️22 = a + 4d

✔️22 = a + 4 (5/2 a ) (the value which we found above for d )

✔️22 = a + 2 * 5 a ( 4 and 2 will get cancelled)

✔️22 = a + 10 a

✔️22 = 11a

✔️a = 2

✔️d =5/2 a

✔️d = 5/2*2

✔️d = 5

✔️Now the AP is: 2,7,12,17,22,27.

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