Find the 19th term !

Algebra Level pending

The fourth term of an arithmetic progression is 92 92 and the tenth term is 80 80 . Find the 1 9 t h 19^{th} term.


The answer is 62.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

a n = a m + ( n − m ) d a_n=a_m+(n-m)d

80 = 92 + ( 10 − 4 ) d 80=92+(10-4)d

d = − 2 d=-2

Thus,

a 19 = a 10 + ( 19 − 10 ) d = 80 + ( 9 ) ( − 2 ) = a_{19}=a_{10}+(19-10)d=80+(9)(-2)= 62 \boxed{62}

or

a 19 = a 4 + ( 19 − 4 ) d = 92 + ( 15 ) ( − 2 ) = a_{19}=a_4+(19-4)d=92+(15)(-2)= 62 \boxed{62}

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