In an AP, if the third term is 15 and sum of ten terms is 125, find the common difference
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jiab7a9neshshaswin
jiab7a9neshshaswin
19.02.2016
Math
Secondary School
+10 pts
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In an A.P. GIVEN a3=15 ,S10=125, find d and a10
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josimagic Ambitious
Answer:
d = -1 and a10 = 8
Step-by-step explanation:
Formula:-
nth term of AP, tn = a + (n-1) d
Sum of n terms Sn = n/2[2a + (n-1)d]
a - first term and d = common difference
To find a and d
It is given that, a3=15 ,S10=125
We can write a + 2d = 15 ----(1)
10/2[2a + 9d ] = 125
⇒5[2a + 9d ] = 125
⇒2a + 9d = 25 ----(2)
(1)*2 ⇒ 2a + 4d = 30 ---(3)
(2) - (3) ⇒
5d = -5
d = -1
eq (1) ⇒ a + 2d = 15
a + -1*2 = 15
a = 15 + 2 = 17
To find a10
a10 = a + 9d = 17 + 9*-1 = 17 - 9 = 8
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