Question

If in an AP A10 = and a45 = 140 find the common difference

Answer 1

Step-by-step explanation:

Given A.P is

1,−2,−5,−8,....

hence the common difference is given by d=an+1−an

by putting n=1 in above equation

d=a2−a1=(−2)−(1)

d=(−2−1)

d=−3

first term of this A.P is

a1=1

the nth term of this A.P is given by

an=a1+(n−1)d

⟹an=1+(n−1)(−3)

⟹an=1−3n+3

⟹an=4−3n….eq(1)

finding next four terms of A.P

1)     for finding the 5th term of sequence (a5)  put n=5 in eq(1)

⟹a5=4−3×5

⟹a5=4−15

⟹a5=−11

2)    for finding the 6th term  of sequence (a6) put n=6 in eq(1)

⟹a