Question

The sum of first 14 terms of an A.P. is 1050 and its 14th term is 140. Find its 20th term​

Answer 1

Answer:

Answer is 200

Step-by-step explanation:

Here,

S14 = 1050

n = 14,

a = 10

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

1050 = 14/2 [20 + 13d]

1050 = 140 + 91d

910 = 91d

d = 10

Therefore,

a20 = 10 + (20 – 1) × 10 = 200

The 20th term is 200.

Answer 2

Answer:

20th term = 200

Step-by-step explanation:

$14th \: term = 140 \\ a + 13d = 140 \\ sum \: of \: first \: 14 \: terms \: = 140 \\ 14(a + a + 13d) \div 2 = 1050 \\ 14(a + 140) = 1050 \times 2 \\ a + 140 = 2100 \div 14 \\ a + 140 = 150 \\ a = 10 \\ a + 13d = 140 \\ 13d = 140 - 10 \\ d = 130 \div 13 \\ d = 10 \\ 20th \: term = a + 19d \\ = 10 + 19 \times 10 \\ = \: 200$