If the sum of first 14 terms of an AP is 1050 and its first term is 10, then its 20th term is :
Answer & explanation
Correct answer: option 1
Sum of first 14 terms of an AP (Sn) = 1050
n = 14
First term ( a ) = 10
We know,
Sn = \(\frac{n}{2}\)[ 2a + (n-1)d]
1050 = \(\frac{14}{2}\)[ 2 × 10 + (14-1)d]
1050 = 7[ 20 + 13d]
1050 = 140 + 91d
d = 10
Now,
20th term = a + ( n - 1 ) d
= 10 + ( 20 - 1 ) × 10
= 10 + 190
= 200