Given that the first term of an A.P is 7 and its 10th term is twice its second calculate a)19th term b) sum of 28 term c) different between the 9th and 6th term
1st term = 7, 2nd term = a+d = 7+d. Then, since 10th term is twice it second, it implies 10th term = a+9d = 7+9d = 2(7+d). Open the bracket and collect like terms we have, 9d-2d = 14-7. Then 7d = 7. Finally, d = 1. (a) the 19th terms = a+18d = 7+18(1) = 25. (b) the sum of 28th term = n/2[2a + (n-1)d] = 28/2[2(7) + (27(1)] = 574. Hence, to solve for (c), find the 9th term and the 6th term separately, then take the difference of the answers. You will have 15-12 = 3.
a=7
a+9d=2(a+d)
7+9d=2(7+d)
7+9d=14+2d
14-7=9d-2d
7÷7=7d÷7
d=1
1. a+18d
7+18(1)
=25
2. Sn=n÷2[2a+(n-1)d]
28÷2[2(7)+(28-1)1]
14[14+27]
14[41]
=574
3. 9th term=a+8d
7+8(1)
=15
6th term=a+5d
7+5(1)
=12
Difference=15-12=3
7 ,7+r, *, *, *, *, *, *, *, 14+2r,
Term n = 7 +r(n-1)
term 10 = 7 +9 r = 14 + 2 r
so 7 r = 7
r = 1
and we have
7 ,8, 9, 10, 11, 12, 13, 14, 15, 16,
n = 19
term 19 = 7 + 1(18) =25
a)T19=12
b)S28=48
Good And Happy
Once
To solve this problem, we need to use the formula to find the nth term of an arithmetic progression (A.P):
a(n) = a(1) + (n - 1)d
where:
a(n) is the nth term,
a(1) is the first term, and
d is the common difference.
Given that the first term (a(1)) is 7, we can substitute this value into the formula:
a(n) = 7 + (n - 1)d
We are also given that the 10th term (a(10)) is twice the second term (a(2)). Let's use this information to find the common difference (d).
a(10) = 2 * a(2)
7 + (10 - 1)d = 2 * (7 + (2 - 1)d)
7 + 9d = 14 + 2d
7d = 7
d = 1
Now that we have the common difference, we can find the 19th term (a(19)) by substituting the values into the formula:
a(19) = 7 + (19 - 1) * 1
a(19) = 7 + 18
a(19) = 25
Therefore, the 19th term is 25.
To find the sum of the first 28 terms (S(28)), we can use the formula for the sum of an A.P:
S(n) = (n/2)(a(1) + a(n))
Substituting the values:
S(28) = (28/2)(7 + 25)
S(28) = 14(32)
S(28) = 448
Therefore, the sum of the first 28 terms is 448.
The difference between the 9th term (a(9)) and the 6th term (a(6)) can be found by substituting the values into the formula:
a(9) = 7 + (9 - 1) * 1
a(9) = 7 + 8
a(9) = 15
a(6) = 7 + (6 - 1) * 1
a(6) = 7 + 5
a(6) = 12
The difference between a(9) and a(6) is:
a(9) - a(6) = 15 - 12
a(9) - a(6) = 3
Therefore, the difference between the 9th and 6th terms is 3.