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

1790

Emily

Pari

Answer / Solution

Answer / Solution

Solution: Given that,

first term, a = 5

last term, l = 45

Sum of the AP, S_{n} = 400

As we know, the sum of AP formula is;

S_{n} = 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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