21)
[tex] a_{n} [/tex] = a₁ + d(n - 1) ; where a₁ is the first term and d is the difference.
a₁ = 3, d = 4 → [tex] a_{n} [/tex] = 3 + 4(n - 1) = 3 + 4n - 4 = 4n - 1
[tex] a_{25} [/tex] = 4(25) - 1 = 100 - 1 = 99
[tex] S_{n} [/tex] = [tex] \frac{a_{1} +a_{n} }{2}(n) [/tex]
[tex] S_{25} [/tex] = [tex] \frac{3 +99 }{2}(25) [/tex] = [tex] \frac{102 }{2} (25) [/tex] = 51 · 25 = 1275
Answer: [tex] a_{n} [/tex] = 4n - 1 , 1275
23)
[tex] a_{n} [/tex] = a₁ + d(n - 1) ; where a₁ is the first term and d is the difference.
a₁ = 4, d = 10 → [tex] a_{n} [/tex] = 4 + 10(n - 1) = 4 + 10n - 10 = 10n - 6
[tex] a_{25} [/tex] = 10(25) - 6 = 250 - 6 = 244
[tex] S_{n} [/tex] = [tex] \frac{a_{1} +a_{n} }{2} (n) [/tex]
[tex] S_{25} [/tex] = [tex] \frac{4 +244 }{2} (25) [/tex] = [tex] \frac{248}{2}(25) [/tex] = 124 · 25 = 3100
Answer: [tex] a_{n} [/tex] = 10n - 6 , 3100
