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For a given G.P., if T5 = 405 and T7 = 3645; then find T4.

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T5 = 405, T7 = 3645, T4 =?

Tn = a.rn-1

∴ T5 = a. r4

∴ 405 = a. r4 ……….(1)

T7 = a. r6

∴ 3645 = a. r6 ………(2)

T4 = a. r3 …….(3)

Taking the ratio of results (2) and (1),

\(\frac{3645}{405}=\frac{ar^6}{ar^4}\)

∴ 9 = r2

∴ r = ± 3

Putting r = ± 3 In result (1),

405 = a (± 3)4

∴ 405 = a × 81

∴ a = 405 / 81 = 5

Putting a = 5 and r = ±3 In result (3).

T4 = 5(±3)3

∴ T4 = 5 (± 27)

∴ T4 =± 135

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