Find the first six terms of the sequence. a₁ = -4, a_n = a_{n - 1} + 7

Solution:

Given, the series is in arithmetic progression

First term, a₁ = -4

a_n = a_{n - 1} + 7

We have to find the six terms of a finite sequence.

Arithmetic progression can be represented by the formula,

a_n = a + (n-1)d

Here common difference is 7,

\(a(2) = a_{2-1}+7= a_{1}+7=-4+7=3\)

\(a(3) = a_{3-1}+7= a_{2}+7=3+7=10\)

\(a(4) = a_{4-1}+7= a_{3}+7=10+7=17\)

\(a(5) = a_{5-1}+7= a_{4}+7=17+7=24\)

\(a(6) = a_{6-1}+7= a_{5}+7=24+7=31\)

Therefore, the six terms are -4, 3, 10, 17, 24 and 31.

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Find the first six terms of the sequence. a₁ = -4, a_n = a_{n - 1} + 7

Summary:

The first six terms of the sequence. a₁ = -4, a_n = a_{n - 1} + 7 are -4, 3, 10, 17, 24 and 31.