Question

Find Sn for the following arithmetic sequences described.

Answer 1

See below for all answers and explanations

Explanation:

Problem A

`\displaystyle S_n=(n)/(2)(a_1+a_n)=(25)/(2)(4+100)=12.5(104)=1300`

Problem B

`a_n=a_1+(n-1)d\\52=132+(n-1)(-4)\\52=132-4n+4\\52=136-4n\\-84=-4n\\n=21\\\\\displaystyle S_n=(n)/(2)(a_1+a_n)=(21)/(2)(132+52)=10.5(184)=1932`

Problem C

`a_n=a_1+(n-1)d\\a_n=4+(n-1)(6)\\a_n=4+6n-6\\a_n=6n-2\\106=6n-2\\108=6n\\n=18\\\\\displaystyle S_n=(n)/(2)(a_1+a_n)=(18)/(2)(4+106)=9(110)=990`

Problem D

`\displaystyle S_n=(n)/(2)(a_1+a_n)\\\\108=(n)/(2)(3+24)\\\\108=(n)/(2)(27)\\\\216=27n\\\\n=8\\\\\\a_n=a_1+(n-1)d\\24=3+(8-1)d\\21=7d\\d=3\\\\\\a_n=3+(n-1)(3)\\a_n=3+3n-3\\a_n=3n\\\\a_1=3 \leftarrow \text{First Term}\\a_2=3(2)=6\leftarrow \text{Second Term}\\a_3=3(3)=9\leftarrow \text{Third Term}`

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