Question

Which term of the AP -3,3,9….. is 117

Answer 1

Given:-

⠀⠀⠀◍ AP = -3 , 3 , 9 ......

⠀⠀⠀◍ an = 117

⠀⠀

To find:-

⠀⠀⠀◍ The value of n.

⠀⠀

Identity used:-

⠀⠀⠀◍ an = a+ (n -1) d.

⠀⠀

Solution:-

⠀⠀⠀◍ Value of d = a2 - a1

⠀⠀⠀◍ d = 3 - (-3)

⠀⠀⠀◍ d = 6

⠀

⠀⠀⠀✯ an = a + (n - 1)d

⠀⠀⠀✯ 117 = -3 + (n - 1)6

⠀⠀⠀✯ 117 + 3 = 6n - 6

⠀⠀⠀✯ 120 + 6 = 6n

⠀⠀⠀✯ $\sf\dfrac{\cancel{126}}{\cancel{6}}$

⠀⠀⠀✯ n = 21

⠀⠀

Answer:-

⠀⠀⠀★ 21st term of an AP -3 , 3 , 9 , ..... is

⠀⠀⠀⠀ 117.

Answer 2

$\tt\underline{Given:-}$

⠀⠀⠀◍ $\tt{AP\: = \:-3 \:, \:3 \:, \:9\: ......}$

⠀⠀⠀◍ $\tt{an \:=\: 117}$

⠀⠀

$\tt\underline{To\:\:find:-}$

⠀⠀⠀◍ $\tt{The\:\: value\:\: of \:\:n.}$

⠀⠀

$\tt\underline{Formula\:\:used:-}$

⠀⠀⠀◍ $\tt{an\: = \:a+\: (n\: -\:1) \:d.}$

$\tt\underline{Solution:-}$

⠀⠀⠀◍ $\tt{Value \:of\: d \:= \:a2\: - \:a1}$

⠀⠀⠀◍ $\tt{d \:=\: 3\: -\: (-3)}$

⠀⠀⠀◍ $\tt{d = 6}$

⠀⠀

⠀⠀⠀✯ $\tt{an\: = \:a\: +\: (n\: - \:1)d}$

⠀⠀⠀✯ $\tt{117\: =\: -3 \:+\: (n \:- \:1)6}$

⠀⠀⠀✯ $\tt{117\: +\: 3\: =\: 6n\: - \:6}$

⠀⠀⠀✯ $\tt{120 \:+ \:6 \:= \:6n}$

⠀⠀⠀✯ $\sf\dfrac{\cancel{126}}{\cancel{6}}$⠀✯ $\tt{n\: = \:21}$

$\tt\underline{Answer:-}$

⠀⠀⠀★ $\tt{21st\:\: term\:\: of \:\:an \:\:AP}$

⠀⠀⠀$\tt{\:\:-3 \:\:, \:\:3 \:\:, \:\:9\:\: ,\:\: ..... is \:\:117.}$