The 6th and 11th term of an AP are 23 and 48 respectively. Calculate the sum of the first 20 terms of sequence?

1 Answer
Apr 20, 2018

#S_20=910#

Explanation:

# a_6=23 , a_11=48 ; a_n= a_1+(n-1)d#

#:. a_6= a_1+(6-1)d or a_1+5 d =23 (1) #

#:. a_11= a_1+(11-1)d or a_1+10 d =48 (2) #

#(2)-(1): 5 d= 25 :. d = 5 , a_1+ 5*5=23 :. a_1= -2#

Sum of sequence : #a_1=-2, d=5 , n=20#

#S_n=n/2 {2 a_1+(n-1)d}# or

#S_20=20/2 {2*(-2)+(20-1)5}= 10(-4+95)=910# [Ans]