Question

The first and last term of ap are1 & 11 if the sum of their term is 36 then what is the no of terms

Answer 1

Number of terms = 6

GivEn:-

• First term of AP (a) = 1

• Last term of AP ($\sf a_n$) = 11

• Sum of thier term ($\sf S_n$) = 36

To find:-

• Number of terms (n) = ?

Solution:-

We have,

• a = 1

• $\sf a_n$ = 11

• $\sf S_n$ = 36

Therefore,

Sum of n terms of AP :-

$\dag\;{\underline{\boxed{\bf{\blue{ S_n = \dfrac{n}{2} \bigg( a + l \bigg)}}}}} \\ \\ :\implies\sf 36 = \dfrac{n}{2} \bigg( 1 + 11 \bigg) \\ \\ :\implies\sf 36 \times 2 = n(12) \\ \\ :\implies 72 = 12n \\ \\ :\implies\sf n = \cancel{ \dfrac{72}{12}} \\ \\ :\implies {\underline{\boxed{\bf{\pink{ n = 6}}}}}$

$\dag$ Hence, 36 is the sum of 6 terms of AP.

$\rule{150}{4}$

$\dag$ Additional Information:-

Here,

We can also find the common difference from each term of AP,

★ Putting the Value of n in:-

$\star\;\;\bf a_n = a + (n - 1)d \\ \\ \dashrightarrow\sf 11 = 1 + ( 6 - 1 )d \\ \\ \dashrightarrow\sf 11 = 1 + 5d \\ \\ \dashrightarrow\sf 11 - 1 = 5d \\ \\ \dashrightarrow\sf 10 = 5d \\ \\ \dashrightarrow\sf d = \cancel{ \dfrac{10}{5}} \\ \\ \dashrightarrow {\underline{\boxed{\bf{\red{d = 2}}}}}$

$\rule{150}{4}$