Respuesta :
Answer:
- The sum of the first 30 terms of this arithmetic sequence is 209. Hoped this helped.
Step-by-step explanation:
We know that:
- Formula = 6 + (7x)
Work:
- => 6 + (7x)
- => 6 + {7(29)}
- => 6 + 203
- => 209
Hence, the sum of the first 30 terms of this arithmetic sequence is 209. Hoped this helped.
[tex]BrainiacUser1357[/tex]
Answer:
The sum of first 30 terms of arithmetic sequence is 3225.
Step-by-step explanation:
Here's the required formula to find the sum of the arithmetic sequence :
[tex] \star{\underline{\boxed{\sf{S_n = \dfrac{n}{2}\Big[2a + (n - 1)d\Big]}}}}[/tex]
- [tex]\pink\star[/tex] Sₙ = number of terms of AP
- [tex]\pink\star[/tex] n = n terms of AP
- [tex]\pink\star[/tex] d = common difference of AP
- [tex]\pink\star[/tex] a = first term of AP
Substituting all the given values in the formula to find the sum of arithmetic sequence :
- [tex]\blue\star[/tex] Sₙ = 30
- [tex]\blue\star[/tex] n = 30
- [tex]\blue\star[/tex] d = 7
- [tex]\blue\star[/tex] a = 6
[tex]{\implies{\sf{S_n = \dfrac{n}{2}\Big[2a + (n - 1)d\Big]}}}[/tex]
[tex]{\implies{\sf{S_{30} = \dfrac{30}{2}\Big[2 \times 6 + (30 - 1)7\Big]}}}[/tex]
[tex]{\implies{\sf{S_{30} = \dfrac{30}{2}\Big[12+ (29)7\Big]}}}[/tex]
[tex]{\implies{\sf{S_{30} = \dfrac{30}{2}\Big[12+ 29 \times 7\Big]}}}[/tex]
[tex]{\implies{\sf{S_{30} = \dfrac{30}{2}\Big[12+203\Big]}}}[/tex]
[tex]{\implies{\sf{S_{30} = \dfrac{30}{2}\Big[ \: 215 \: \Big]}}}[/tex]
[tex]{\implies{\sf{S_{30} = 15\Big[ \: 215 \: \Big]}}}[/tex]
[tex]{\implies{\sf{S_{30} = 15 \times 215}}}[/tex]
[tex]{\implies{\sf{S_{30} = 3225}}}[/tex]
[tex] \star{\underline{\boxed{\sf{S_{30} =3225}}}}[/tex]
Hence, the sum of first 30 terms of arithmetic sequence is 3225.
[tex]\rule{300}{2.5}[/tex]
