One of the most important question from ML Aggarwal we have been given that if sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, then find the sum of first 10 terms.
Please give me a detailed solution of this question
ML Aggarwal (avichal publication)
Class 10 Arithmetic Progression
Chapter 9 question no 11
Given,
36=26[2a+(6−1)d]
12=2a+5d ———(1)
256=216[2a+(16−1)d]
32=2a+15d ———(2)
Subtracting, (1) from (2)
32−12=2a+15d−(2a+5d)
20=10d ⟹d=2
Substituting for d in (1),
12=2a+5(2)=2(a+5)
6=a+5 ⟹a=1
∴ The sum of first 10 terms of an AP,
S10=210[2(1)+(10−1)2]
S10=5[2+18]
S10=100