Question

The first three terms of an A.P. are x+2x+1 and 5x-1. Find x and the sum of the first 10 terms.

Answer 1

First three terms of AP = X, 2X+1 and 5X-1

since these are consecutive terms of the same AP, their common difference is same.

therefore,

2X+1 - X = 5X-1 - 2X - 1

X+1 = 3X-2

2X = 3

X = 3/2

therefore, first term = 3/2  second term = 2*3/2 + 1 = 4

common difference = 4 - 3/2 = 5/2

sum of fist ten terms = S10 = 10/2 [2*3/2 + 9*5/2]

5 [3 + 45/2]

5 [6+45/2]

5 [51/2]

255/2 = 127.5

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