Question

Find the number of terms of the A.P.
41, 38, 35, ..., 8?

Answer 1

Given

Find the number of terms of the A.P.

41, 38, 35, ..., 8

Solution

⠀ ⠀⠀

Tn → a + ( n - 1 ) d

where ,

a → first term

d → common difference

Here ,

a :- 41

d :- 38 - 41 → -3

Tn :- 8

Therefore ,

➵ 8 → 41 + ( n - 1 ) ( -3 )

➵ 8 → 41 - 3 ( n - 1 )

➵ 8 → 41 - 3n + 3

➵ 3n → 41 + 3 - 8

➵ 3n → 44 - 8

➵ 3n → 36

➵ n → 12

Hence , there are 12 terms in the AP 41 , 38 , 35 , ... , 8 .

⠀ ⠀

Answer 2

${\sf{\underline{Given\::}}}$

${\bullet \:{\sf{A.P.\:=\:41, 38, 35, ... , 8 }}}$

${\bullet \:{\sf{First\:term\:, a\:=\:41}}}$

${\bullet \:{\sf{Last\:term\:=\:8}}}$

${\bullet \:{\sf{Common\:difference\:=\:38\:-\:41\:=\:-3}}}$

${\sf{\underline{To\:Find}}}$

${\bullet \:{\sf{Number\:of\:terms(n)}}}$

${\sf{\underline{Solution}}}$

$⠀⠀⠀⠀\bold{\boxed{\sf{\red{Last\:term\:=\:a\:+\:(n\:-\:1)d}}}}$

$\leadsto \sf 8\:=\:41\:+\:(n\:-\:1)(-3)$

$\leadsto \sf 8\:-\:41 \:=\: (n\:-\:1)(-3)$

$\leadsto \sf -33\:=\: -3n\:+\:3$

$\leadsto \sf -33\:-\:3 \:=\:-3n$

$\leadsto \sf -36 \:=\: -3n$

$\leadsto \sf n\:=\: \cancel \dfrac{-36}{-3}$

$\leadsto \sf n\:=\: 12$

• Number of terms = 12

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