Question

The first term of an A.P. is 5, the last term is
45 and the sum of all its terms is 400. Find the
number of terms and the common difference
of the A.P
(AI 2017. Delhi 2014)
answer fast guys​

Answer 1

Answer:

Step-by-step explanation:

using

sum=n/2(a+l)

a= first term of the AP

l= last term of the AP

n= number of terms

substituting the values

400=n/2(5+45)

after solving we get

number of terms=16

we know that the 16th term is 45 (i.e. last term)

using

a= (n-1)d

a=45

n=16

substituting the values we get,

45= 15d

common difference= 3

hope you found it helpful.

Answer 2

Answer:

a= 5 ,L = 45 , sn= 400

d= ?, n=?

an = a + (n-1)d

45 = 5 + (n-1)d

45-5 = (n-1 )d

40 = (n-1)d

40d =n-1 _________eq.1

sn = n/2(2a+(n-1)d

400 = n/2 (2×5+(n-1) d

400 = n/2 ( 10 + (n-1) d

400×2 = n ( 10+ (n-1)d

800 = (10n + n^2 -n )d

800= (9n + n^2)d ________2

so we get d = 2

amd n =16

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