amswer it fast........
Share
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Answer:
It will need 14 terms.. In an A. P.
Verified answer
☯ AnSwEr :
(5).
First term (a) = 12
Sixth term of A.P (a6) = a + 5d = 8 .....(1)
★ Put value of a in equation 1.
→ a + 5d = 8
→ 12 + 5d = 8
→ 5d = 8 - 12
→ 5d = -4
→ d = -4/5
Now, we know that
[tex]\Large{\implies{\boxed{\boxed{\sf{S_n = \frac{n}{2} \bigg(2a + (n - 1)d \bigg)}}}}}[/tex]
★ Putting Values ★
[tex]\sf{\dashrightarrow 120 = \frac{n}{2} \bigg(2(12) + (n - 1) \times \frac{-4}{5} \bigg)} \\ \\ \sf{\dashrightarrow 120 \times 2 = n \bigg(24 + (n - 1) \times \frac{-4}{5} \bigg)} \\ \\ \sf{\dashrightarrow 240 = 4n \bigg(6 + (n - 1) \frac{-1}{5} \bigg)} \\ \\ \sf{\dashrightarrow \frac{240}{4} = n( 6 + \frac{-1n}{5} + \frac{1}{5}} \\ \\ \sf{\dashrightarrow 60 = n( 6 + \frac{30 + -n + 1}{5}} \\ \\ \sf{\dashrightarrow 60 = n(\frac{31 - n}{5})} \\ \\ \sf{\dashrightarrow 60 \times 5 = 31n - n^2} \\ \\ \sf{\dashrightarrow -n^2 + 31n - 300 = 0} \\ \\ \sf{\dashrightarrow n^2 - 31n + 300 = 0}[/tex]
[tex]\rule{200}{2}[/tex]
(6).
A.P : 12, 18, 24 ........ 96
First term (a) = 12
Common Difference (d) = 6
Last term (An) = 96
We know that,
[tex]\Large{\implies{\boxed{\boxed{\sf{A_n = a + (n - 1)d}}}}}[/tex]
★ Putting Values ★
[tex]\sf{\dashrightarrow 96 = 12 + (n - 1)6} \\ \\ \sf{\dashrightarrow 96 - 12 = (n - 1)6} \\ \\ \sf{\dashrightarrow \frac{84}{6} = n - 1} \\ \\ \sf{\dashrightarrow n - 1 = 14} \\ \\ \sf{\dashrightarrow n = 15} \\ \\ \Large{\implies{\boxed{\boxed{\sf{n = 15}}}}}[/tex]