If the eight term of an arithmetic sequence with first term -1 is 20, then what is the common difference?
The first and last terms of an arithmetic sequence with thirteen terms are -7 and -115, respectively. Find the sum of the sequence.
Please answer both questions and explain the steps,
thankyou.
1) F + (N - 1)*D=Nth Term, where F=First term, D=Common difference and N=Number of terms.
-1 + (8 - 1)*D =20, solve for D
-1 + 7D = 20
7D = 20 + 1
7D =21 divide both sides by 7
D = 21 / 7
D = 3 Common difference
2)
(F + L) / 2*N, where F=First term, L=Last term and N=Number of terms.
Sum = (-7 - 115) / 2*13
Sum =( -122 / 2) * 13
Sum = -61 * 13
Sum = -793
1) F + (N - 1)*D=Nth Term, where F=First term, D=Common difference and N=Number of terms.
-1 + (8 - 1)*D =20, solve for D
-1 + 7D = 20
7D = 20 + 1
7D =21 divide both sides by 7
D = 21 / 7
D = 3 Common difference
2)
(F + L) / 2*N, where F=First term, L=Last term and N=Number of terms.
Sum = (-7 - 115) / 2*13
Sum =( -122 / 2) * 13
Sum = -61 * 13
Sum = -793