Advertisements
Advertisements
Question
Find the middle term of the AP 6, 13, 20, …., 216.
Solution
The given AP is 6,13,20,........,216.
First term, a = 6
Common difference, d =13- 6 = 7
Suppose these are n terms in the given AP. Then,
an = 216
⇒ 6+(n-1) × 7 = 216 [ an = a + (n-1) d]
⇒ 7 (n-1) = 216 -6 =210
⇒ n-1`=210/7 =30`
⇒ n= 30+1 =31
Thus, the given AP contains 31 terms,
∴ Middle term of the given AP
`=((31+1)/2)`th term
= 16th term
= 6+ (16-1) × 7
= 6+105
=111
Hence, the middle term of the given AP is 111.
APPEARS IN
RELATED QUESTIONS
Find the sum of first 30 terms of an A.P. whose second term is 2 and seventh term is 22
The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.
Find how many integers between 200 and 500 are divisible by 8.
Find the sum of all odd natural numbers less than 50.
Find the sum of first n even natural numbers.
Choose the correct alternative answer for the following question.
For an given A.P. a = 3.5, d = 0, n = 101, then tn = ....
Q.12
Kanika was given her pocket money on Jan 1st, 2008. She puts Rs 1 on Day 1, Rs 2 on Day 2, Rs 3 on Day 3, and continued doing so till the end of the month, from this money into her piggy bank. She also spent Rs 204 of her pocket money, and found that at the end of the month she still had Rs 100 with her. How much was her pocket money for the month?
If 7 times the seventh term of the AP is equal to 5 times the fifth term, then find the value of its 12th term.
