In an arithmetic sequence the sum of the 5th and 7th term is 38 and the sum of the first 15 terms is 375. Calculate the sum of the next 15 terms ? How can one solve this ?

Question

2011 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-06T02:31:20

#color(blue)("Sum of 16th to 30th terms " = S_30 - S_15 = 1050#

#"Sum of 5th and 7th terms = " 38#

#"Sum of first 15 terms = " 375#

#"To find sum of 16th to 30th terms"#

#a_5 + a_7 = 38#

#a_5 = a_1 + (5-1) * d#

#a_n = a_1 + (7-1) * d #

#a_5 + a_7 = 2 a_1 + 10 d #

#38 = 2 a_1 + 10d#

#19 = a_1 + 5d, " Eqn 1"#

#S_n = (n * (a_1 + a_n) ) / 2#

#S_15 = (15 * (a_1 + (a_1 + (15-1) * d))) / 2#

#375 = (30 a_1 + 210 d) / 2 = 15 a_1 + 105 d#

#25 = a_1 + 7 d, " Eqn 2"#

Solving Equations 1 & 2,

#a_1 = 4, d = 3#

#a_30 = a_1 + (30-1) * d#

#a_30 = 4 + 29*3 = 91#

#"Sum of first 30 terms " S_30 = (30 * (a_1 + a_30)) / 2#

#S_30 = (30 * (4 + 91)) / 2 = 1425#

#"Sum of 16th to 30th terms " = S_30 - S_15 = 1425 -375 = 1050#