We have the progression
91, 85, 79, ..., -29.
Also we can test:
85 - 91 = -6
79 - 85 = - 6
Hence, the progression is an arithmetic progression with d = -6.
Now, using the general formula of an arithmetic progression, we can find the position of term -29; as follows:
[tex]\begin{gathered} a_n=a_1+(n-1)\times d_{} \\ -29\text{ = 91 + (n - 1)(-6) } \end{gathered}[/tex]So n = 21
Now we know -29 is the term on the 21 position, we can proceed to find the sum of the first 21st terms of the progression:
[tex]S_n\text{ = }\frac{a_1+a_n}{2}n\text{ }[/tex]Solving the formula we have:
[tex]S_{21}\text{ = }\frac{91-29_{}}{2}\text{ x 21 }[/tex]S₂₁ = 651
