Sum of the first 3 term of an AP is 300 and the sum of first
7 term is 140 Find the sum of first 10 term.
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Answer:
- 220
Step-by-step explanation:
a, a + d, a+2d...... a + (n-1) d...are in AP
sum of first three terms of AP = 300
a + a +d+ a+2d=300
3(a+d) =300
a+d=100-----> i
sum of first 7 term = 140
a+a+d + a +2d+ a+3d+ a +4d+ a+5d+a+6d=140
7a+21d=140
a+3d= 20-------->ii
ii - i
a + 3d = 20
a + d = 100
- - -
___________
2d = - 80
d = - 40
from I
a-40= 100
a = 100 + 40
a = 140
sum first n terms = a + (n-1) × d
= 140+(10-1)×(-40)
=140 + 9×(-40)
=140 - 360
= - 220
the sum of first 10 terms= - 220
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