Find the sum of the first five terms of the arithmetic sequence with first term 3 and common difference 5 .

Short Answer

Expert verified
Answer: The sum of the first five terms of the arithmetic sequence is 65.

Step by step solution

01

Find the nth term of the arithmetic sequence

To find the nth term of an arithmetic sequence, we can use the formula a_n = a_1 + (n - 1) * d, where a_n is the nth term, a_1 is the first term, n is the number of terms, and d is the common difference. In this case, we have a_1 = 3, d = 5 and n = 5. a_n = 3 + (5 - 1) * 5
02

Calculate the nth term

Calculate the value of the nth term: a_n = 3 + (4) * 5 a_n = 3 + 20 a_n = 23
03

Use the sum formula for arithmetic sequences

To find the sum of the first five terms, we will use the formula S_n = n * (a_1 + a_n) / 2, where S_n is the sum of the first n terms, a_1 is the first term, a_n is the nth term, and n is the number of terms. Plug in the values we have: S_5 = 5 * (3 + 23) / 2
04

Calculate the sum

Calculate the sum of the first five terms: S_5 = 5 * (26) / 2 S_5 = 130 / 2 S_5 = 65 The sum of the first five terms of the arithmetic sequence is 65.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Study anywhere. Anytime. Across all devices.

Sign-up for free