Question

In an A. P if an=3+4n then the value of a3 is. What?

Answer 1

Answer:

an=3−4n [Given]

∴a1 =3−4(1)=−1

a 2=3−4(2)=−5

a 3=3−4(3)=−9

a4 =3−4(4)=−13

Now, d1 =a2−a1 =−5−(−1)=−4

d2=a3−a2=−9−(−5)=−4

d3=a4−a3=−13−(−9)=−4

As d1=d 2 =d 3 =−4 so a 1 ,a 2 ,a 3 ...a n are in A.P.

So, a = -1, d = -4, n = 20

Now, S

n= 2n

up [2a+(n−1)d]

⇒S

20

=

2

20

[2×(−1)+(20−1)(−4)]

⇒S

20

=−780

Hence, a

1

,a

2

,a

3

...a

n

are in A.P. and S

20

=−780