Question

If the sum of the first 14 terms of an A.P. is 1050 and its first term is 10, find the 20th term. ​

Answer 1

Answer:

200

Step-by-step explanation:

Number of terms, n = 14

Sum of the 14 terms = 1050

First term, a = 10

$S_{n}$ = $\frac{n}{2}$(2a + (n - 1)d)

1050 = 14/2 (2*10 + (14-1)d)

1050 = 7 (20+13d)

1050/7 = 20+13d

150 = 20 + 13d

150-20 = 13d

130= 13d

10 = d

$a_{20}$ = a+(n-1)d

    = 10 + (20-1)10

    = 10 + 19*10

    = 10+190

    = 200

Answer 2

Answer:

Step-by-step explanation:

Given that,

1st term of an A. P. = a = 10

The sum of the first 14 terms of an A. P.

S14 = 1050

By using formula,

S14 = 14/2 [ 2 × 10 + ( 14 - 1 ) d ] [∵Sn = n/2 [2a + ( n - 1 ) d ] ]

1050 = 7 ( 20 + 13d )

1050 / 7 = 20 + 13d

150 = 20 + 13d

150 - 20 = 13d

130 = 13d

130/13 = d

d = 10.

∴20th term of an A. P.

a20 = a + 19d

= 10 + 19 × 10

= 10 + 190

= 200 is the answer.