Question

First termm and last form of an ap are 1 and 11 if
the sum of all its terms is 36 then find the
number of terms in the AP​

Answer 1

Step-by-step explanation:

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Answer 2

$\bf{\Huge{\boxed{\sf{\pink{ANSWER\::}}}}}$

$\bf{\Large{\underline{\bf{Given\::}}}}}$

• First term of an A.P.[a] = 1
• Last term of an A.P.[l] = 11
• Sum of all its term = 36.

$\bf{\Large{\underline{\bf{To\:find\::}}}}$

The number of term in the A.P.

$\bf{\Large{\underline{\tt{\green{Explanation\::}}}}}$

We know that formula of nth term;

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

So,

$\mapsto\sf{1+(n-1)d=11}$

$\mapsto\sf{(n-1)d\:=\:11-1}$

$\mapsto\sf{(n-1)d\:=\:10.................(1)}$

Formula of the sum of the A.P.

$\leadsto\tt{Sn\:=\:\frac{n}{2} [2a+(n-1)d]}$

Putting equation (1) in above formula, we get;

$\mapsto\sf{\frac{n}{2} [2*1+10]=36}$

$\mapsto\sf{\frac{n}{2} (12)=36}$

$\mapsto\sf{12n\:=\:36*2}$

$\mapsto\sf{12n\:=\:72}$

$\mapsto\sf{n\:=\:\cancel{\frac{72}{12} }}$

$\mapsto\sf{\orange{n\:=\:6}}$

Thus,

The number of terms in the A.P. is 6.