Find the sum of a finite arithmetic sequence from n = 1 to n = 13, using the expression 3n + 3.

Solution:

A sequence is finite if it has a limited number of terms

From the given sum n = 1 and n = 13

So the given sequence is finite.

For the standard form of arithmetic sequence a, a + d, a + 2d, a + 3d……l, the first term is a and the last term is ’ l’

Comparing with the standard form

If n = 1 in 3n + 3 gives the first term a

If n = 13 in 3n + 3 gives the last term l

a = 3 (1) + 3 = 6

l = 3(13) + 3 = 39 + 3 = 42

If a is the first term and l is the nth term of an arithmetic sequence, the sum of the sequence is given by (n/2){(a + l)}

Sum of the finite sequence from n = 1 to n = 13 with nth term as 3n + 3 is

(13/2) × {6 + 42}

Sum of the finite sequence = (13/2) × 48 = 13 × 24 = 312

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Find the sum of a finite arithmetic sequence from n = 1 to n = 13, using the expression 3n + 3.

Summary :

Sum of a finite arithmetic sequence from n = 1 to n = 13 using the expression 3n + 3 is 312.