Question

Find the common difference of the A.P. and write the next two terms: $75,67,59,51,.....$

Answer 1

Given A.P is,

$75,67,59,51,...\dots$

first term of this A.P is $a_1=75$

second term of this A.P is $a_2=67$

third term of this A.P is $a_3=59$

fourth term of this A.P is $a_4=51$

common difference of an A.P is $(i.e.,d=a_{n+1}-a_n)$

putting n=1 in above equation

$d=a_2-a_1=67-75=-8$

hence,common difference $d=-8$

we know that nth term of an A.P is given by

$a_n=a_1+(n-1)d$

$⟹a_n=75+(n-1)(-8)$

$⟹a_n=75-8n+8$

or

$⟹a_n=83+8n\dots ..eq\left(1\right)$

for finding next two terms

for 5th term $a_5$ put n=5 in eq(1)

$⟹a_5=83-8\times 5$

$⟹a_5=83-40$

$⟹a_5=43$

for 6th term $a_6$ put n=6 in eq(1)

$⟹a_6=83-8\times 6$

$⟹a_6=83-48$

$⟹a_6=35$