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