Question

14.In an Arithmetic Progression, if a=2,-4, n-7. then as is:
(a) 4
(b) 5
(c) 30
(d)-22​

Answer 1

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)

⟹a6

Answer 2

(d) -22

Explanation:

Here, a = 2

d = -4

n = 7

aₙ = ?

Now; aₙ = a + (n-1)d

= 2 + (7-1)×-4

= 2+6×-4

= 2-24

= -22 Ans.

I hope this helps.