rk2640152
Answered

Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Find the nth term for the following question: -5,-2,3,10,19​

Sagot :

MrRoyal

Answer:

[tex]T_n = 2n - 1 + T_{n-1}[/tex]

Step-by-step explanation:

Given

[tex]Sequence: -5,-2,3,10,19[/tex]

Required

Find the nth term

We have:

[tex]T_1 = -5[/tex]

[tex]T_2 = -2 = 3 - 5 = 3 + T_1[/tex]

[tex]T_3 = 3 = 5 - 2 = 5 + T_2[/tex]

[tex]T_4 = 10 = 7 + 3 = 7 +T_3[/tex]

[tex]T_5 = 19 = 9 + 10 = 9 + T_4[/tex]

This gives:

[tex]T_2 = 3 + T_1 = 4 - 1 + T_1[/tex]

[tex]T_3 = 5 + T_2 = 6 - 1 + T_2[/tex]

[tex]T_4 = 7 +T_3 = 8 - 1 + T_3[/tex]

[tex]T_5 = 9 + T_4 = 10 - 1 + T_4[/tex]

---

Solving further, we have:

[tex]T_2 = 4 - 1 + T_1 = 2 * 2 - 1 + T_1[/tex]

[tex]T_3 = 6 - 1 + T_2 = 2 * 3 + T_2[/tex]

[tex]T_4 = 8 - 1 + T_3 = 2 * 4 - 1 + T_3[/tex]

[tex]T_5 = 10 - 1 + T_4 = 2 * 5 - 1 + T_4[/tex]

Following the above sequence: the nth term is:

[tex]T_n = 2n - 1 + T_{n-1}[/tex]

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.