In 9th term of the series 1 + 5 + 13 + 29 + ...... is given by

Question

In $9^{t h}$ term of the series 1 + 5 + 13 + 29 + ...... is given by

Smart Achievers · Accepted Answer

(4)

$1 + 5 + 13 + 29 + \dots$

$First difference 4, 8, 16, \dots \in G.P.$ $∴$ $r = 2$

$∴$ $t_{n} = a + b r^{n - 1} = a + b {(2)}^{n - 1}$

$∴$ $n = 1,$ $n = 2$

$we get$ $a + b = 1$ $and$ $a + 2 b = 5$

$a = - 3,$ $b = 4$

$∴$ $t_{n} = a + b r^{n - 1} = 4 {(2)}^{n - 1} - 3$

$∴$ $t_{9} = 4 \cdot 2^{8} - 3 = 1024 - 3 = 1021$

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