Question

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

Answer 1

Given A.P is,

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

first term of this A.P is $a_1=51$

second term of this A.P is $a_2=59$

third term of this A.P is $a_3=67$

fourth term of this A.P is $a_4=75$

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

putting n=1 in above equation

$d=a_2-a_1=59-51=8$

hence,

common difference $d=8$

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

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

$⟹a_n=51+(n-1)8$

$⟹a_n=51+8n-8$

or

$⟹a_n=43+8n\dots ..eq\left(1\right)$

for finding next two terms

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

$⟹a_5=43+8\times 5$

$⟹a_5=43+40$

$⟹a_5=83$

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

$⟹a_6=43+8\times 6$

$⟹a_6=43+48$

$⟹a_6=91$