Problem

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, $a_{1}$, and common difference, $d$. Find $a_{150}$ when $a_{1}=-40, d=5$

Solution

Step 1 :Given the first term, $a_{1}=-40$, and common difference, $d=5$, of an arithmetic sequence, we are to find the 150th term, $a_{150}$.

Step 2 :We use the formula for the nth term of an arithmetic sequence, which is $a_{n} = a_{1} + (n-1)d$.

Step 3 :Substitute the given values into this formula: $a_{150} = -40 + (150-1)\times5$.

Step 4 :Simplify the expression to get $a_{150} = -40 + 149\times5$.

Step 5 :Calculate the result to get $a_{150} = 705$.

Step 6 :\(\boxed{705}\) is the 150th term of the sequence.

From Solvely APP
Source: https://solvelyapp.com/problems/20786/

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