Question

the first term of an ap is 5 the last term is 45 and the sum is 400 find the number of terms and the common difference

Answer 1

S n= n/ 2( a+l )
here a = 5, l = 45
put value in formula
400 = n/2 (5+45)
400 = n/2(50)
400(2)/50 = n
800/50 = n
by solving this ,we get
n = 16
so number of terms = 16
again And = n/2 ( 2a+ ( n -1 ) d
400 = 16/2(2(5) + (n - 1) d
400 = 8 (10+(16-1) d
400 = 8(10 +15d)
400/8 = 10+15 d
50 = 10+15d
50-10 = 15d
40/15 = d
8/3 = d
this is your answer

Answer 2

hey, here is your answer.....

given, first term(a) = 5..,
last term(l) = 45.., sum(Sn) = 400..,

then, Sn = (n/2)(a+l)....

400 = (n/2)(5+45)...

800 = n(50)....

n = (80/5)....

n = 16......

therefore, no. of terms = 16....

l = a+(n-1)d.....

45 = 5+(15)d...

40 = 15d.....

d = 8/3....


therefore common difference is 8/3....




hope this helps you....
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