For an AP the first term is 4 and last term is 31 the sum of all the term is 420 what is value of n

n = 24

Step-by-step explanation:

From the question,

The formula for the sum of the term in an AP is given as

Sₙ = n(a+L)/2 Equation 1

Where Sₙ = sum of the nth term, n = number of term, a = first term, L = last term.

make n the subject of the equation

n = 2Sₙ/(a+L) Equation 2

Given: Sₙ = 420, a = 4, L = 31

Substitute these values into equation 2

n = (2×420)/(4+31)

n = (840)/35

n = 24.

Hence, n = 24

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