Question

For a given arithmetic sequence, the common difference, d, is equal to 4, and the 3rdterm, a3, is equal to 19.Find the value of the 77th term, a77.a77=

Answer 1

Step-by-step explanation

From the statement, we have an arithmetic sequence with:

• common difference d = 4,

,

• 3rd term a₃ = 19.

We must find the 77th term.

(1) The general formula for the nth term of an arithmetic sequence is:

`a_n=a_1+(n-1)\cdot d.`

Replacing the data from above, we have:

`a_n=a_1+4(n-1).`

(2) We compute the a₁. Replacing the n = 3 and a₃ = 19, we have:

`\begin{gathered} a_3=a_1+4(3-1), \\ 19=a_1+8. \end{gathered}`

Solving for a₁, we get:

`a_1=19-8=11.`

Replacing this value in the general formula, we have:

`a_n=11+4(n-1).`

(3) Evaluating the general formula for n = 77, we get the 77th term of the sequence:

`a_(77)=11+4\cdot(77-1)=11+304=315.`Answer

a₇₇ = 315