The first term of finite A. P. Is 15, the last term is 45 and the sum of all term is 500 find the number of term
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In the AP, a = 10
Tn = 50 = a+(n-1)d = 10+(n-1)d, or (n-1)d = 40.
Sn = 480 = (n/2)[2a+(n-1)d]
= (n/2)[2*10+40]
= (n/2)[20+40) = 30n
or n = 480/30 = 16.
So the AP consists of 16 terms.
Check: 50 = 10+(16–1)d = 10+15d, 15d = 40, or d = 40/15 or 8/3
S16 = (16/2)[2*10+40) = 8[20+40]=8*60 = 480.
Tn = 50 = a+(n-1)d = 10+(n-1)d, or (n-1)d = 40.
Sn = 480 = (n/2)[2a+(n-1)d]
= (n/2)[2*10+40]
= (n/2)[20+40) = 30n
or n = 480/30 = 16.
So the AP consists of 16 terms.
Check: 50 = 10+(16–1)d = 10+15d, 15d = 40, or d = 40/15 or 8/3
S16 = (16/2)[2*10+40) = 8[20+40]=8*60 = 480.
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