Sn= n/2 (a+L). Know how to Prove it??

bubble_gum_pop

if u can spare a min tht wud b great :smile:

i need to know how to prove the formula: Sn = n/2(a+L)

Reply 1

SsEe

Sn = n/2 [2a + (n-1)d] = n/2(a + (a+(n-1)d)) = n/2(a+L)

Reply 2

bubble_gum_pop

thx

Reply 3

Speleo

Sn = a + (a+d) + ... + (a+(n-2)d) + (a+(n-1)d)
Sn = (a+(n-1)d) + (a+(n-2)d) + ... + (a+d) + a
2Sn = [a+(a+(n-1)d)] + [a+d+(a+(n-2)d] + ... + [(a+(n-2)d)+a+d] + [(a+(n-1)d) + a]
2Sn = (2a+(n-1)d) + (2a+(n-1)d) + ... + (2a+(n-1)d) + (2a+(n-1)d)
2Sn = n(2a+(n-1)d)
Sn = (n/2)(2a+(n-1)d)

Then use what SsEe said.