Answer:
The first term is 6; the common difference in 0.8.
Step-by-step explanation:
The nth term is:
[tex] a_n = a_1 + (n - 1)d [/tex]
The sum of the first n terms is:
[tex] S_n = \dfrac{n(a_1 + a_n)}{2} [/tex]
[tex] a_{n} = a_1 + (n - 1)d [/tex]
[tex] a_{11} = a_1 + (11-1)d [/tex]
[tex] a_1 + 10d = 14 [/tex] Equation 1
[tex] S_n = \dfrac{n(a_1 + a_n)}{2} [/tex]
[tex] S_{26} = \dfrac{26(a_1 + a_{26})}{2} [/tex]
[tex] \dfrac{26(a_1 + a_1 + 25d}{2} = 416 [/tex]
[tex] \dfrac{52a_1 + 650d)}{2} = 416 [/tex]
[tex] 26a_1 + 325d = 416 [/tex] Equation 2
Equation 1 and Equation 2 form a system of equations in 2 unknowns.
To eliminate a_1, subtract 26 times Eq. 1 from Eq. 2.
[tex] 65d = 52 [/tex]
[tex] d = \dfrac{52}{65} [/tex]
[tex] d = \dfrac{4}{5} = 0.8 [/tex]
[tex] a_1 + 10d = 14 [/tex]
[tex] a_1 + 10 \times 0.8 = 14 [/tex]
[tex] a_1 + 8 = 14 [/tex]
[tex] a_1 = 6 [/tex]
Answer:
The first term is 6; the common difference in 0.8.
