Question

If A= 1-2+3-4+5+.......+99
B=2+4+6+8+.......+100
Then the value of A +B is

Answer 1

A+B = 1+3+5......99+100

A+B = 50/2( 2+ 49×2) +100

A+B = 25( 2+ 98) +100

A+B = 2500 +100
A+B = 2600

Answer 2

Answer:

2600

Step-by-step explanation:

Given: A= 1-2+3-4+5+.......+99

B=2+4+6+8+.......+100

To find: A+B

Solution:

The nth term of an arithmetic sequence is determined using the arithmetic sequence formula. Recall that a sequence is a series of numbers in a specific order. The total of the terms in a sequence makes up a series.. An arithmetic progression or series is one in which each term is produced or attained by adding or deducting a common number from the term or value that comes before it. In other words, the difference in the arithmetic sequence between consecutive terms is the same.

Solving the series A,

A=1-2+3-4+5+.......+99

A=I-II

$I:\\a_1=1\\d=2\\a_n=99\\a_n=a+(n-1)d\\99=1+(n-1)2\\n=50\\S_n=\frac{50}{2} [2+(49)(2)]\\S_n=25000$

$II:\\a_1=2\\d=2\\a_n=98\\S_n=\frac{49}{2}[2a+(n-1)d]\\ S_n=\frac{49}{2}[(2)(2)+(48)(2)]\\S_n=2450\\A=I-II\\2500-2450=50$

$B=2+4+6+8+........+100\\a=2\\d=2\\a_n=100\\100=2+(n-1)2\\n=50\\S_n=\frac{50}{2}[4+(49)(2)]\\ =2550$

Thus A+B = 2550+50

=2600

Hence the correct answer is 2600.

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