Advertisements
Advertisements
Question
If the nth term of a progression is (4n – 10) show that it is an AP. Find its
(i) first term, (ii) common difference (iii) 16 the term.
Solution
`T_n = (4_n - 10 ) ` [Given]
`T_1 = (4xx 1 - 10 ) = -6`
`T_2 = (4xx2-10)=-2`
`T_3 = (4xx3 -10 ) =2`
`T_4= ( 4xx4-10) =6`
Clearly,[-2 -(-6)]=[2-(-2)] = [6-2] = 4 (Constant)
So, the terms - 6,-2,2,6,...... forms an AP.
Thus we have
(i) First term = - 6
(ii) Common difference = 4
(iii)` T_16 = a + ( n-1) d= a + 15d = -6 + 15 xx 4 =54`
APPEARS IN
RELATED QUESTIONS
Write the first five terms of the following sequences whose nth terms are:
`a_n = (3n - 2)/5`
Which term of the A.P. 3, 8, 13, ... is 248?
An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find the 32nd term.
The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 34. Find the first term and the common difference of the A.P.
Which term of the A.P. −4, −1, 2, ... is 101?
20th term of the AP -5, -3, -1, 1, is ______.
For the AP: –3, –7, –11, ..., can we find directly a30 – a20 without actually finding a30 and a20? Give reasons for your answer.
If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18th term will be ______.
Justify whether it is true to say that the following are the nth terms of an AP.
3n2 + 5
Fill in the blank in the following table, given that a is the first term, d the common difference, and an nth term of the AP:
| a | d | n | an |
| -18.9 | 2.5 | ______ | 3.6 |
