Question

An arithmatic progression has
its 5th term 30 and 9 term
54 find the series​

Answer 1

Answer:

Question:-

An Arithmetic progression has its 5th term 30 and 9th term 54;find the sequence of A.P.

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Required Answer:-

Given:- t5=30

t9=54

To find:- sequence of A.P.

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Solution:-

1) t5=30-(given)

tn=a+(n-1)d

t5=a+(5-1)d

30=a+4d

a+4d=30-(i)

2) t9=54-(given)

tn=a+(n-1)d

t9=a+(9-1)d

54=a+8d

a+8d=54-(ii)

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3) subtracting equation (i) and (ii)

a+4d=30 -(i)

-a-8d= -54 -(ii)

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-4d= -24

4d= 24

d=24/4

d=6

4) put d=6 in equation (i)

a+4d=30

a+4(6)=30

a+24=30

a=30-24

a=6

5) First term of an A.P. is a=6

6) Common difference(d)=6

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7) Now, to find the sequence of

A.P., find next terms by using formula:-

t2= t1+d

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8) t2=t1+d

t2=6+6 -(from 4 and 3)

t2=12

9) t3=t2+d

t3=12+6-(from 8 and 4)

t3=18

10) t4=t3+d

t4=18+6 -(from 9 and 4)

t4=24

11) Therefore, Sequence of an A.P. is 6,12,18,24.......

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Hope it help you.