Question

The first and the last terms of an A.P. are 5 and 45 respectively. If the sum of all its terms is 400, find its common difference.

Answer 1

Answer:

The number of terms is 16 and the common Difference is 8/3 .

Step-by-step explanation:

Given :  first term , a = 5, last term, l = 45 and Sn = 400

By using the formula ,Sum of nth terms , Sn = n/2 [a + l]

Sn = n/2 [5  + 45]

400 = n/2 [5  + 45]]  

400 = n/2 × 50

400 = 25n

n = 400/25

n = 16

Number of terms, n = 16

So,Last term is 16th term .

a16 = 45

By using the formula ,an = a + (n - 1)d

a + (16 - 1)d = 45

a + 15d = 45

5 + 15d = 45

[Given ,a = 5]

15d = 45 - 5

15d = 40

d = 40/15

d = 8/3

Common Difference ,d = 8/3  

Hence,the number of terms is 16 and the common Difference is 8/3 .

HOPE THIS ANSWER WILL HELP YOU.

Answer 2

Answer:

Step-by-step explanation:

Hope that helps ubout.. .