let a1,a2 and b1,b2 - Maths - Arithmetic Progressions

Question

let a1,a2 and b1,b2
be the arithmetic progressions such that a1=25
b1=75 and a100+b100=100 find the
sum of first 100 terms of the
progression(a1+b1),(a2+b2)

priyanka saggu · Accepted Answer

Given A P: a1, a2  and b1, b2
 The first term of both A
P: a1 = 25 and b1 = 75and the sum of 100th term of both the A
P i e
 (a100 + b100)= 100According to question:As we know, Sum of nth term of an A
P is Sn=n2a+lWhere, n = number of termsa = First term of A
Pl = Last term of A
PHere, for the new A
P: (a1 + b1), (a2 + b2)
(a100 + b100)The first term is (a1 + b1) = 25+75=100And, the last term is (a100 + b100)= 100Therefore, Sn=n2(a1 + b1)+ (a100 + b100)= 1002100+100=10000

let a1,a2.......... and b1,b2............be the arithmetic progressions such that a1=25 b1=75 and a100+b100=100.find the sum of first 100 terms of the progression(a1+b1),(a2+b2)

let a₁,a_{2.......... and} b₁,b_{2............}be the arithmetic progressions such that a₁=25 b₁=75 and a₁₀₀+b₁₀₀=100.find the sum of first 100 terms of the progression(a₁+b₁),(a₂+b₂)