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In an A.P. the first term is –5 and last term is 45. If sum of all numbers in the A.P. is 120, then how many terms are there? What is the common difference?
Print or SaveSol. For the given A. P.
First term a = –5
tn = 45
Sn = 120
∴ tn = a + (n –1)d
45 = –5 + (n –1)d
45 + 5 = (n –1)d
(n –1)d = 50 ...(I)
Sn = \({n\over2}[2a+(n-1)d]\) [Formula]
120 = \({n\over2}[2*(-5)+50]\) [From (I)]
240 = n [ –10 + 50]
240 = n × 40
n = 6
Place n = 6 in eqn. (I)
(6 – 1)d = 50
d = \(50\over 5\)
d = 10
∴ There are 6 terms in the A. P. and the common difference is 10.