The 14th term of cm AP is 96 while the 25th term is 173 from. (a)19th term (b)sum of 13th and 56th term (c)product of 6th and 13th term
Google math is fun arithmetic sequence
a , a+d, a+ 2d , ..... a + (n-1) d
if n = 14
a + 13 d = 96
if n = 25
a + 24 d = 173
so
a - a + (13-24)d = 96-173
-11 d = - 77
d = 7 whew, whole number, the rest is easy :)
25
To find the solutions of the given questions, we can first find the common difference (d) of the arithmetic progression (AP). Then, we can use the formula for the nth term of an AP:
nth term (Tn) = a + (n-1) * d
where Tn is the nth term, a is the first term, n is the term number, and d is the common difference.
Given information:
14th term (T14) = 96
25th term (T25) = 173
Step 1: Finding the common difference (d)
We have two equations using the formula for the nth term:
T14 = a + (14-1) * d --> Equation 1
T25 = a + (25-1) * d --> Equation 2
Subtracting Equation 1 from Equation 2 will eliminate the 'a' term:
T25 - T14 = [(a + (25-1) * d) - (a + (14-1) * d)]
173 - 96 = (25-1)d - (14-1)d
77 = 24d - 13d
77 = 11d
Dividing both sides by 11:
d = 77/11
d = 7
So, the common difference (d) is 7.
Step 2: Using the nth term formula to find the solutions
(a) Finding the 19th term:
T19 = a + (19-1) * d
= a + 18d
Since we do not know the value of 'a', we need more information.
(b) Finding the sum of the 13th and 56th terms:
Sum of the terms = T13 + T56
= (a + (13-1) * d) + (a + (56-1) * d)
= 2a + 12d + 55d
= 2a + 67d
Again, since we do not know the value of 'a', we need more information.
(c) Finding the product of the 6th and 13th terms:
Product of the terms = T6 * T13
= (a + (6-1) * d) * (a + (13-1) * d)
= (a + 5d) * (a + 12d)
= a^2 + 17ad + 60d^2
Like before, we need more information to determine the exact value of a, so we cannot calculate the product.
In summary:
(a) The 19th term cannot be determined without additional information.
(b) The sum of the 13th and 56th term cannot be determined without additional information.
(c) The product of the 6th and 13th term cannot be determined without additional information.