# arthmetic

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in an arthmetic progression or series,the 13th term is 27 and the 7th iterm is 3 times the 2nd term ,find first term the common difference the sum of rhe squence

• arthmetic -

13th term is 27 --- a + 12d = 27

the 7th iterm is 3 times the 2nd term --> a+6d = 3(a+d)
or
a+6d = 3a + 3d
2a = 3d
a = 3d/2
sub into the first equation
3d/2 + 12d = 27
3d+24d=54
d = 2
then a = 3(2)/2 = 3

I will let you finish it for the sum, you did not say how many terms you want to add.

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