Question

the first term of an A. P is5 and the last term is 45 if the sum of all terms is400. find the number of terms??
​

Answer 1

Answer :

The required number of terms = 16

Step-by-step explanation :

Given :

In an A.P.,

• first term, a = 5
• last term, n = 45
• sum of all terms, Sₙ = 400

To find :

the number of terms

Solution :

 nth term of an A.P. is given by,

  $\underline{\boxed{\bf a_n=a+(n-1)d}}$

Substitute the values,

  45 = 5 + (n - 1)d

  (n - 1)d = 45 - 5

  (n - 1)d = 40

Sum of n terms is given by,

 $\underline{\boxed{\bf S_n=\dfrac{n}{2}[2a+(n-1)d]}}$

Substitute the values,

  $\sf 400=\dfrac{n}{2}[2(5)+(n-1)d]$

 400 × 2 = n [ 10 + (n - 1)d ]

 800 = n [ 10 + (n - 1)d ]

 

Substitute (n - 1)d = 40

 800 = n [ 10 + 40 ]

 800 = n [ 50 ]

 n = 800/50

 n = 80/5

 n = 16

∴ The number of terms = 16