Question

Find 21st term of an A.P. whose 17th term is 52 and 11th term is 70.

Answer 1

ANSWER:

• 21st term = 40

GIVEN:

• 17th term = 52
• 11th term = 70

TO FIND:

• Value of 21st term.

SOLUTION:

Nth term of an A.P

=> nth term = a+(n-1)d

Where :

a = First term

d = Common difference.

n = number of terms.

=> 17th term = 52

=> a+(17-1)d = 52

=> a+16d = 52 .....(i)

=> 11th term = 70

=> a+(11-1)d = 70

=> a+10d = 70 .....(ii)

Subtracting eq(ii) from (i)

=> 16d-10d = 52-70

=> 6d = -18

=> d = -18/6

=> d = -3

Putting d = -3 in eq(i)

=> a -48 = 52

=> a = 52+48

=> a = 100

Now :

=> 21st term = 100+(21-1)(-3)

=> 21st term = 100-60

=> 21st term = 40

Answer 2

Answer:

40

Step-by-step explanation:

17th term,

a+16d=52

11th term,

a+10d=70

Then,a=100 ,d=-3

21th term,

a+(n-1)d=100+(20)(-3)

=100-60

=40