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a level maths help exam paper question

the tenth term of an arithmetic series is 67 and the sum of the first twenty terms is 1280. find the first term a and the common difference d.
Reply 1
Avatar for Qk_Sol
Qk_Sol
Un= a + (n-1)d
67 = a + 9d -------- Eq (1)

Sn= (n/2)*(2a+(n-1)d)
1280 = (20/2)*(2a+19d)
1280 = 10*(2a + 19d)
128 = 2a + 19d ------- Eq(2)

Solving simultaneously,

Eq(1) * 2,

134 = 2a + 18d -------- Eq(3)

Eq(3) - Eq(2)

6 = -d
d = -6

Solving for a,

67 = a + 9(-6)
a = 121
Reply 2
Avatar for Ewan
Ewan
15
Qk_Sol
1


:facepalm: Don't give full solutions. "Help" doesn't mean "give me the answer" :s-smilie:
Reply 3
Avatar for Qk_Sol
Qk_Sol
oh well! Sorry, next time I won't. But I hope you understand fully how I got the answer. If u do, u should be able to solve almost all questions of this kind.
Reply 4
Avatar for Pheylan
Pheylan
sammy3000
the tenth term of an arithmetic series is 67 and the sum of the first twenty terms is 1280. find the first term a and the common difference d.

i like these questions

Spoiler

Reply 5
Avatar for douchebagz
douchebagz
1
Qk_Sol
Un= a + (n-1)d
67 = a + 9d -------- Eq (1)

Sn= (n/2)*(2a+(n-1)d)
1280 = (20/2)*(2a+19d)
1280 = 10*(2a + 19d)
128 = 2a + 19d ------- Eq(2)

Solving simultaneously,

Eq(1) * 2,

134 = 2a + 18d -------- Eq(3)

Eq(3) - Eq(2)

6 = -d
d = -6

Solving for a,

67 = a + 9(-6)
a = 121


Where'd you get 9d from? :s-smilie:
Reply 6
Avatar for Pheylan
Pheylan
douchebagz
Where'd you get 9d from? :s-smilie:

first term of an arithmetic series = a
second term = a + d
third term = a + 2d
nth term = a + (n - 1)d
Reply 7
Avatar for sammy3000
sammy3000
OP
hi thanks for the solution.

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