Question

find the 31st term of an AP whose 10th term is 30 and the 15th term is 65​

Answer 1

Answer:

177

Step-by-step explanation:

a31=??

a31=a+30d

a10=30 (Given)

a+9d=30

a=30-9d -----(1)

a15=65 (Given)

a+14d=65 -----(2)

putting the value of a from eq.(1) in eq.(2)

a+14d=65

30-9d+14d=65

30+5d=65

5d=65-30

5d=35

d=35/5

d=7

putting the value of d in eq.(1) we will get the value of a

a=30-9d

a=30-9(7)

a=30-63

a=-33

We know that a31=a+30d....

Now,put the values of a and d

a31= -33+30(7)

a31= -33+210

a31= 177