Question

which term of the AP 21,18,15,...is -96

Answer 1

Answer: 4p

Step-by-step explanation:

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Answer 2

$\large\bf\underline{Given:-}$

• An AP is given as 21,18,15,...

$\large\bf\underline {To \: find:-}$

• which term of ap is -96.

$\huge\bf\underline{Solution:-}$

• AP = 21,18,15,...

• first term = 21
• common difference = 18-21 = -3

$\large \bf \: a_n = a + (n-1)d$

$: \implies \rm \: - 96= 21 + (n - 1) - 3 \\ \\ : \implies \rm \: - 96 - 21 = (n - 1) - 3 \\ \\ : \implies \rm \: - 117 =( n - 1) - 3 \\ \\ : \implies \rm \cancel\dfrac{ - 117}{ - 3} = n - 1 \\ \\ : \implies \rm \:39 = n - 1 \\ \\ : \implies \bf \:n = 40$

So,

40th term is -96.

$\large \bf \underline{Verification:-}$

⠀⠀⠀⠀⠀➝ 40th term = a + 39d

⠀⠀⠀⠀⠀➝ 40th term = 21 + 39 ×-3

⠀⠀⠀⠀⠀➝ 40th term = 21 - 117

⠀⠀⠀⠀⠀➝ 40th term = -96

So,

we get -96 which is the 40th term of the given AP .

Hence Verified.