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Question
In an AP, the first term is -4, the last term is 29 and the sum of all its terms is 150. Find its common difference.
Solution
Suppose there are n terms in the AP.
Here , a = 4 , l = 29 and sn = 150
sn = 150
`⇒ n/2 (-4 +29 ) = 150 [ s_n = n/2 (a+l) ]`
` ⇒ n = (150xx 2) / 25 = 12`
Thus, the AP contains 12 terms.
Let d be the common difference of the AP.
∴ a12 = 29
⇒ - 4 + (12-1) × d = 29 [ an = a+(n-1)d]
⇒ 11d = 29 +4 = 33
⇒ d= 3
Hence, the common difference of the AP is 3.
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