The 3rd term of an AP is 10 more than the first term while the fifth term is 15 more than the second term.find the sum of the 8th and 15 term of AP.if the 7th term is seven times the first term.
a saturated solution of salt X contain0.28g of the salt in 100cm3 of solution at 25degree centigrate, what is the solubility of the salt X at this temperature (R.m.m of X=56)
Let the 1st term be "a" and the 2nd term be "a+d" then 3rd term = a+2d = 10+a(i.e 10 more than the 1st term) and 5th term = 15+a+d(i.e 15 more than the 2nd term). Then 2d = 10(from 1st statement). This implies that d =5. Then the 7th term = a+6d =7a(7 times the 1st term). 6a = 6d =6(5) =30. Hence, a =30/6 = 5. Also, 8th term = a+7d =5+7(5) = 40 and 15th term = a+14d = 5+14(5) = 75. Finally their sum is 40+75 = 115. Thanks
Gdh
I don't understand the way in which the solving is
I mean I don't understand the answer
To find the sum of the 8th and 15th terms of an arithmetic progression (AP), we first need to find the values of the terms.
Let's assume the first term of the AP is 'a' and the common difference is 'd'.
According to the information given:
- The third term is 10 more than the first term: a + 2d = a + 10
- The fifth term is 15 more than the second term: a + 4d = a + 15
- The seventh term is seven times the first term: a + 6d = 7a
We now have a system of three equations in two variables (a and d). We can solve this system to find their values.
From the first equation, we get:
a + 2d = a + 10
2d = 10
d = 5
Substituting the value of d back into the third equation, we get:
a + 6(5) = 7a
a + 30 = 7a
6a = 30
a = 5
So the first term, 'a', is 5, and the common difference, 'd', is 5.
To find the 8th term of the AP, we use the formula: nth term = a + (n - 1)d
The 8th term, T8, is:
T8 = 5 + (8 - 1) * 5
T8 = 5 + 7 * 5
T8 = 5 + 35
T8 = 40
To find the 15th term of the AP, we use the same formula:
T15 = 5 + (15 - 1) * 5
T15 = 5 + 14 * 5
T15 = 5 + 70
T15 = 75
Now we can find the sum of the 8th and 15th terms:
Sum = T8 + T15
= 40 + 75
= 115
Therefore, the sum of the 8th and 15th terms of the AP is 115.