Question

If the $5$th term of an A.P is $31$ and $25$th term is $140$ more than the $5^{th} term, find the first term of the A.P.

Answer 1

Let a be the first term and d be the common difference.

Then $a_5=31$

$a+4d=31$ _____ (1)

$a_{25}=140+a_5$

$a+24d=140+31=171$ ________ (2)

subtracting (1) from (2)

$20d=140$

$d=7$

Put $d=7$ in (1)

$a+28=31$

Thus $a=3$