Question

in an A.P the sum of 1 st ,3rd,5th term is,39 and the sum of 2nd,4th and 6th term is 51 find 10th term of the,sequence

Answer 1

The sum of the 4th and 6th terms of an arithmetical progression is 42. The sum of the 3rd and 9th terms of the progression is 52. How do I find the first term, common difference, and sum of the ten terms of the progression?

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7 ANSWERS



Adhiraj Dare, I love Mathematics

Answered Jan 7, 2015 · Author has 173answers and 268.9k answer views

Assuming the first term to be `a` and the common difference to be `d`.

nth term is given by a + (n-1)d

Thus:

a+3d +a +5d = 42 ; a+4d=21
a+2d + a + 8d =52; a+5d= 26
 
Therefore, d=5 and a=1.
 
First term is, a=1
Tenth term is, a+9d= 46
 
Sum of first 10 terms = 10/2*(1+46) = 235

Answer 2

a+(1-1)d+a+(3-1)d+a+(5-1)d=39
3a+6d=39
a+2d=13--------------eq1
a+(2-1)d+a+(4-1)d+a+(6-1)d=51
a+d+a+3d+a+5d=51
3a+9d=51
a+3d=17------------eq2
from eq1 AND2
a+2d=13
a+3d=17
- - -
--------------
-d=-4
d=4


by putting value of d in eq 1
a+2d=13
a+8=13
a=5




10th term =a+(n-1)d
10th=5+36
10th=41