Question

The first and last term of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be *

Answer 1

Answer:

Number of terms = 6

Step-by-step explanation:

Given:

• First term = a = 1
• Last term = aₙ = 11
• Sum of terms = Sₙ = 36

To find:

Number of terms = n = ?

Solution:

For solving such questions where the first and last term are given, we use this formula.

$\maltese \: \: \boxed{ \boldsymbol{S_{n} = \dfrac{n}{2}(a + a _{n})}}$

Substitute the given values.

$\implies \sf{36 = \dfrac{n}{2} \big(1 + 11)}$

$\implies \sf{36 = \dfrac{n}{2}(12) }$

$\implies \sf{36 = \dfrac{12n}{2} }$

$\implies \sf{36 = 6n}$

$\implies \sf{n = \dfrac{36}{6} }$

$\implies \sf{n = 6}$

∴ The number of terms = 6

Answer 2

Step-by-step explanation:

given :

The first and last term of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be *

to find :

the number of terms will be *

solution :

• a= 1

• L= 11

• Sn = 36

• n( a +L)/2 = 36 => n(1+11)= 72

• n × 12 = 72

• n = 6

• No.of terms = 6

Hope it help you