Question

Find the sum of the following AP
(a) 2 +4 +6 +....+ 98 +100
(b) (-5) +(-10) +(-15) +...+ (-50)

Answer 1

(a) In this arithmetic progression, the first term is 2, the common difference is 2, and the last term is 100. We can use the formula for the sum of an arithmetic progression:

Sn = (n/2)(a + l)

where Sn is the sum of the arithmetic progression, n is the number of terms, a is the first term, and l is the last term.

In this case, n = (100 - 2)/2 + 1 = 49, a = 2, and l = 100.

Sn = (49/2)(2 + 100)
= (49/2)(102)
= 2499

Therefore, the sum of the arithmetic progression is 2499.

(b) In this arithmetic progression, the first term is -5, the common difference is -5, and the last term is -50. The formula for the sum of an arithmetic progression still applies.

Using the same formula as in part (a):

n = (-50 - (-5))/(-5) + 1 = 10
a = -5
l = -50

Sn = (10/2)(-5 + (-50))
= (10/2)(-55)
= -275

Therefore, the sum of the arithmetic progression is -275.