the first four terms in a sequence are 2, 6, 10, 14. what is the nth term? and what is the sum to n terms of the sequence?

the nth term formula is the sum of the first term (a) and the second to last term (n-1) * the common difference (d). so a + (n-1)d where a = 2 and d = 4 in this case is 2 + (n-1)4 = 4n - 2. the sum to n terms is n/2(2a + (n-1)d) and subbing in the correct values we get n/2(22 + (n-1)*4) = n/2(4 + 4n - 4) = 2n^2. thus we know the sum of any value of n terms of this arithmetic series.

JL
Answered by Jake L. Maths tutor

16477 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

How do you solve a quadratic equation? I always forget how to do that!


How do I solve simultaneous equations?


Solve the simultaneous equation 2x-4y=8 and 3x+3y=-15


On a packet of brown rice it says 'When 60g of rice is cooked, it will weigh 145g.' If Katy has 100g of brown rice, how much will it weigh when cooked?'


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences