the sum of the first 6 term of an ap is 345 and the difference between last and first term is 55 find the terms of AP
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Answer:
30,41,52,63,74,85
Step-by-step explanation:
Given:
Sum of six terms of an AP=345
Difference of first and last term=55
To find: Terms of AP
Solution: Let,
1st Term- a-2d
2nd Term- a-d
3rd Term- a
4th Term- a+d
5th Term- a+2d
6th Term- a+3d
1) According to 1st condition,
(a-2d)+(a-d)+(a)+(a+d)+(a+2d)+(a+3d)= 345
a-2d+a-d+a+a+d+a+2d+a+3d = 345
6a+3d = 345.
According to 2nd condition,
(a+3d) - (a-2d) = 55
a+3d-a+2d = 55
5d = 55
d = 11
2) 1st condition solution - 6a + 3d = 345
6a+3(11) = 345
6a+33 = 345
6a = 312
a = 52
3) Therefore the terms are,
a-2d= 52-22
=30
a-d= 52-11
=41
a= 52
a+d= 52+11
=63
a+2d= 52+22
= 74
a+3d= 52+33
=85
Answer: 30,41,52,63,74,85.
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