Question

Find the 93rd term of the arithmetic sequence -11, -7, -3, ...−11,−7,−3,...

Answer 1

357

Explanation:

Arithmetic sequence is a sequence where the successive terms have a common difference for example

1,2,3,4,5..... is a arithmetic sequence because they have a common difference of one..

Use the arithmetic sequence formula for nth terms.

`a_(1) + (n - 1)d`

Where en is the nth term you trying to find, a1 is the first term of the series and d is the common difference.

a1 is 11, n is 93 and d is 4 so we get

`- 11 + (93 - 1)4`

`- 11 + (92)4`

`- 11 + 368`

`= 357`

Answer 2

The 93rd term of arithmetic sequence is 375.

Step-by-step explanation:

Here's the required formula to find the arithmetic sequence :

`\star\underline{\boxed{\tt{\purple{a_n = a_1 + \Big(n - 1\Big)d}}}}`

• 
  `\blue\star` aₙ = nᵗʰ term
• 
  `\blue\star` a₁ = first term
• 
  `\blue\star` n = number of terms
• 
  `\blue\star` d = common difference

Substituting all the given values in the formula to find the 93rd term of arithmetic sequence :

`\implies{\sf{a_n = a_1 + \Big(n - 1\Big)d}}`

`\implies{\sf{a_(93) = - 11 + \Big(93 - 1\Big)4}}`

`\implies{\sf{a_(93) = - 11 + \Big( \: 92 \: \Big)4}}`

`\implies{\sf{a_(93) = - 11 + 92 * 4}}`

`\implies{\sf{a_(93) = - 11 + 368}}`

`\implies{\sf{a_(93) = 357}}`

`\star{\underline{\boxed{\sf{\red{a_(93) = 357}}}}}`

Hence, the 93rd term of arithmetic sequence is 375.

`\rule{300}{2.5}`