Question

the 9th term of an AP is -32 and the sum of its 11th and 19th term is 94 then find its 20th term​

Answer 1

Answer:

Step-by-step explanation:

Let the first term be a and common difference be d

Thus, 9th term = a+8d = -32  - eqn (1)

11th term = a+10d and 19th term = a+18d

Now, a+10d+a+18d=94

2a+28d=94

a+14d=47 - eqn (2)

Solving eqn (1) and (2):

(-32-8d)+14d=47

6d=47+32

6d=79

d=79/6

Thus, a = 47-14d (from eqn (2)

a=47-14(79/6)

a=-(412/3)

20th term = a+19d = -(412/3)+19(79/6)

20th term = 677/6

Answer 2

Answer:

-5

Step-by-step explanation:

9th term = a+(9-1)d = a+8d = -32--(2)

11th term = a+(11-1)d = a+10d

13th term = a+(13-1)d = a+12d

a+10d+a+12d=-94

2a+22d=-94

a+11d=-47---(1)

(2)-(1):

-3d=15

d=-5

the common difference is equal to -5