Question

Find the sum of the first 6 terms of the sequence: –3, 1, 5, 9, . . .A) 45B) 42C) 48D) 25

Answer 1

From the sequence give

–3, 1, 5, 9, . . .

The first term, a = -3

The common difference, d = 4 (gotten by adding 4 to the next term).

The number of terms required n = 6.

Formula for sum of an arithmetic sequence is given by

`S_n=(n)/(2)\lbrack2a+(n-1)d\rbrack`

Substituting these values into the equation above we have

`\begin{gathered} S_n=(n)/(2)\lbrack2a+(n-1)d\rbrack \\ S_6=(6)/(2)\lbrack2*-3+(6-1)4\rbrack \\ S_6=3\lbrack-6+(5)4\rbrack \\ S_6=3\lbrack-6+20\rbrack \\ S_6=3\lbrack14\rbrack \\ S_6=42 \end{gathered}`

Hence, the answer is 42, option B