The second term of an arithmetic sequence is 7. The sum of the first four terms of the arithmetic sequence is 12. Find the first term, a, and the common difference, d, of the sequence.

Let a be the first term

Let d be the common difference

a + d = 7

S4 = 4/2 (2a +3d) = 12

Simultaneous equation:

a+d =7 // x 6
4a +6d = 12

Difference btween these two

6a + 6d = 42

4a +6d = 12

2a = 30

a = 15

d = 7 -a 

thus d = -8, a = 15

AT
Answered by Alexander T. Maths tutor

20624 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Factorise 3xy+6x^2


How do you solve a simultaneous equation such as x+2y=10 and 3x+2y=18?


How do you use Pythagoras' Theorem?


expand and simplify (x+1)(x-1)


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences