Find the second term - 2

Algebra Level 1

The 6 th 6^\text{th} term of an arithmetic progression is 35.5 35.5 and the 1 7 th 17^\text{th} term is 85. 85. Find the second term.


The answer is 17.5.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Relevant wiki: Arithmetic Progressions

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

We have,

a 17 = a 6 + ( 17 − 6 ) ( d ) a_{17}=a_6+(17-6)(d)

85 = 35.5 + 11 d 85=35.5+11d

d = 4.5 d=4.5

It follows that,

a 2 = a 6 + ( 2 − 6 ) d a_2=a_6+(2-6)d

a 2 = 35.5 + ( − 4 ) ( 4.5 ) = 17.5 a_2=35.5+(-4)(4.5)=\boxed{17.5}

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