The first term of an arithmetic sequence is -4 and its common difference is 5.

Question

MarjTanTyro

Asked: March 30, 20212021-03-30T07:07:39+00:00 2021-03-30T07:07:39+00:00In: Arithmetic, Numbers and Combinatorics, High School/Senior Secondary School

Find its 9th term and the sum of the last 12 terms of the sequence.

You must login to add an answer.

Need An Account,

acedstud · Accepted Answer · 2021-03-30T07:27:21+00:00

Best Answer

acedstud

This answer was edited.

The nth term of an arithmetic sequence is given by $T_n=a+(n-1)d$ , where $a$ is the first term and $d$ is the common difference.

Given: $a=-4$ , $d=5$ .

The 9th term is given by $T_9=-4+(9-1)\times5=-4+8(5)=-4+40=36$ .

The sum of the first n terms of an arithmetic sequence is given by $S_n=\dfrac{n}{2}(2a+(n-1)d$ .

The sum of the first 12 terms is given by $S_{12}=\dfrac{12}{2}(2(-4)+(12-1)\times5)=6(-8+11(5))=6(-8+55)=6(47)=282$ .

First term of the sequence is 10 and common difference is 5.
a1 = -4 and d = 5
Next term = a2=a1+d=-4+5=1
a3=a2+d=1+5=6