Question

7. Find the 31st term of an AP whose 11th term
& An AP consists of 50 terms of which 3rd terme is 12 and the last term is 106. Find the 29th
9. If the 3rd and the oth terms of an AP are 4 and 8 respectively, which term of this AP
term
IS
zero?
7 Find the common difference.​

Answer 1

Step-by-step explanation:

We know that the formula for the nth term is t

n

=a+(n−1)d, where a is the first term, d is the common difference.

It is given that third term of an A.P is t

3

=12, therefore,

t

n

=a+(n−1)d

⇒12=a+(3−1)d

⇒a+2d=12......(1)

Also, it is given that the 50th term is t

50

=106, therefore,

t

n

=a+(n−1)d

⇒106=a+(50−1)d

⇒a+49d=106......(2)

Now, subtract equation 1 from 2 as follows:

(a−a)+(49d−2d)=106−12

⇒47d=94

⇒d=

47

94

=2

Substitute the value of the difference d=2 in equation 1:

a+(2×2)=12

⇒a+4=12

⇒a=12−4=8

Now, the 29th term with a=8 and d=2 can be obtained as:

t

29

=8+(29−1)2=8+(28×2)=8+56=64

Hence, the 29th term is 64.