Write the seventh term of the following GP: 2 | vedclass

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(A) The given sequence is a $GP$ where the first term $a_1 = 21a$.To find the common ratio $r$,we divide the second term by the first term: $r = \frac

Vedclass · Accepted Answer

$86016a^{13}$

Vedclass · Answer

(A) The given sequence is a $GP$ where the first term $a_1 = 21a$.To find the common ratio $r$,we divide the second term by the first term: $r = \frac{84a^3}{21a} = 4a^2$.The $n^{th}$ term of a $GP$ is given by the formula $a_n = a_1 \cdot r^{n-1}$.For the seventh term $(n = 7)$:$a_7 = (21a) \cdot (4a^2)^{7-1}$$a_7 = 21a \cdot (4a^2)^6$$a_7 = 21a \cdot 4^6 \cdot a^{12}$$a_7 = 21 \cdot 4096 \cdot a^{13}$$a_7 = 86016a^{13}$.

Write the seventh term of the following $GP$: $21a, 84a^3, 336a^5, 1344a^7, \dots$

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