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.

Maths

Class 10

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1790

Emily

Pari

Solution: Given that,
first term, a = 5
last term, l = 45
Sum of the AP, Sn = 400

As we know, the sum of AP formula is;
Sn = n/2 (a + l)
400 = n/2 (5 + 45)

400 = n/2 (50)
Number of terms, n = 16

As we know, the last term of AP series can be written as;
Last term, l = a + (n − 1) d
45 = 5 + (16 − 1) d
40 = 15d
Therefore,

Common difference, d = 40/15 = 8/3

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