Question

in an AP the first term is - 4 and the last term is 29 and the sum of all its term is 150 find the common difference

Answer 1

Hey MATE!

a = -4

l = 29

S = 150.

We can apply :

S = n/2[ a + l ]

150 = n/2 [ -4 + 29 ]

300 = n ( 25)

n = 300/25

n = 12


For d we can apply :

29 = -4 + (12 - 1) d

33 = 11 d

d = 3 Answer.

Hope it helps
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Answer 2

first term = a = -4

last term = Tn = 29

sum of the terms = Sn = 150

common difference = d =?
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Tn = a+(n-1)d

150 = -4+(n-1)d

(150+4)/d = n-1

n = (150+5)/d + 1

n = 150+5+d/d

n = (155+d)/d
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Sn = n/2×[a + Tn]

150 = (155+d)/d/2 ×[-4 +29]

150 = (155+d)/2d ×[25]

150×2d = (155+d)25

300d = 3875 + 25d

300d -25d = 3875

275d = 3875

d = 3875/275

d = 155/11
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so , common difference = d = 155/11