find the sum of 25 term of an AP having common difference is 6 and 18t

1.	find the sum of 25 term of an AP having common difference is 6 and 18th term is 110
Answer» the sum of first 25 terms are 2000 An AP hasd = 6a18 = 110 an = a + (n-1)dWhen n = 18a18 = a + (18-1)6110 = a + 17 × 6a + 102 = 110a = 110 - 102a = 8 Sn = n/2 [ 2a + (n-1)d ]When n = 25S25 = 25/2 [ 2×8 + (25-1)6 ]S25 = 25/2 × 2[ 8 + 24×3 ]S25 = 25 ( 8 + 72 )S25 = 25 × 80S25 = 2000

find the sum of 25 term of an AP having common difference is 6 and 18th term is 110

Answer»

the sum of first 25 terms are 2000

An AP hasd = 6a18 = 110

an = a + (n-1)dWhen n = 18a18 = a + (18-1)6110 = a + 17 × 6a + 102 = 110a = 110 - 102a = 8

Sn = n/2 [ 2a + (n-1)d ]When n = 25S25 = 25/2 [ 2×8 + (25-1)6 ]S25 = 25/2 × 2[ 8 + 24×3 ]S25 = 25 ( 8 + 72 )S25 = 25 × 80S25 = 2000