Question

find the 31st term of an ap whose 13th term is 38 and the 16th term is 73 also find s 20

Answer 1

Hey there!
13term = a+12d = 38
16 th term = a+15d = 73 ,

Subtracting the above Two equations,
We get,
3d = 35
d = 35/3 .

a = 38 - 4(35) = 38 - 140 = -102 .

Now,

We know that,
n th term of A. P = a + (n-1)d

31st term of A. P = -102 + (30)(35/3) = -102 + 350 = 248.

Sn [ Sum of n terms ] = n/2 [ 2a + (n-1)d ]

S20 = 20/2 [ 2(-102) + 19(35)/3 ]

= 10 [ -204 + 665/3 ]

= 10 [ - 612 +665/3 ]

= 10 [ 53/3 ]

= 530/3 .

Therefore, 248 , 530/3 are required answers.

Answer 2

hope this helps you☺☺☺☺☺