The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
Answers
No of terms : 16
Common Difference : 8/3
a = 5
l = 45
S = 400
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We know that :
S = n/2 [a + l]
S = n/2 [5 + 45]
400 = n/2 [5 + 45]
400 = n/2 × 50
400 = 25n
n = 400/25
n = 16
Therefore :-
n = 16
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We have the last term and here it is 16 . Therefore :-
a16 = 45
a + (16 - 1)d = 45
a + 15d = 45
5 + 15d = 45
15d = 45 - 5
15d = 40
d = 40/15
Therefore :-
d = 8/3
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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
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 .
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