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Show that the progressions given below i...

Show that the progressions given below is an AP. Find the first term, common difference and next term of each given series.
(1) 9, 15, 21, 27, ….
(ii)11, 6, 1, -4…
(iii)`-1, (-5)/(6), (-2)/(3), (-1)/(2),….`
(iv)`sqrt(2), sqrt(8), sqrt(18), sqrt(32), ....`
`(v)sqrt(20), sqrt(45), sqrt(80), sqrt(125),...`

Text Solution

Verified by Experts

The correct Answer is:
`(i) a=9, d = 6, T_(5) = 33` (ii) a = 11, d = -5, `T_(5)` = -9
(iii) `a = -1, d = (1)/(6), T_(5) = (-1)/(3)` (iv) `a = sqrt(2),d = sqrt(2), T_(5) = sqrt(50)`
`(v) a = sqrt(20), d = sqrt(5), T_(5) = sqrt(180)`

(iv) Given progression is `sqrt(2), sqrt(4 xx 2), sqrt(9 xx 2), sqrt(16 xx 2),..`
i.e., `sqrt(2), 2sqrt(2), 3sqrt(2), 4sqrt(2),…`
`T_(5) = 5sqrt(2) = sqrt(5 xx 5 xx 2) = sqrt(50)`
(v) Given progression is `sqrt(4 xx5), sqrt(9 xx 5), sqrt(16 xx 5), sqrt(25 xx 5),...`
i.e., `2sqrt(5), 3sqrt(5), 4sqrt(5), 5sqrt(5)`,...
`T_(5) = 6sqrt(5) = sqrt(6 xx 6 xx 5) = sqrt(180).`
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