Advertisements
Advertisements
Question
The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20th term.
Advertisements
Solution
Let a be the first term and d be the common difference.
Now, a = 15
Sum of first n terms of an AP is given by,
Sn = `"n"/(2)[2"a" + ("n" - 1)"d"]`
⇒ S15 = `(15)/(2)[2"a" + (15 - 1)"d"]`
⇒ 750 = `(15)/(2)(2"a" + 14"d")`
⇒ a + 7d = 50
⇒ 15 + 7d = 50
⇒ 7d = 35
⇒ d = 5
Now, 20th term = a20
= a + 19d
= 15 + 19 × 5
= 15 + 95
= 110.
RELATED QUESTIONS
Which term of the progression 20, 19`1/4`,18`1/2`,17`3/4`, ... is the first negative term?
Which term of the A.P. `20, 19 1/4, 18 1/2, 17 3/4,` ... is the first negative term?
Choose the correct alternative answer for the following question .
15, 10, 5,... In this A.P sum of first 10 terms is...
If the sum of n terms of an A.P. is 2n2 + 5n, then its nth term is
Find the sum of first 1000 positive integers.
Activity :- Let 1 + 2 + 3 + ........ + 1000
Using formula for the sum of first n terms of an A.P.,
Sn = `square`
S1000 = `square/2 (1 + 1000)`
= 500 × 1001
= `square`
Therefore, Sum of the first 1000 positive integer is `square`
The sum of first 16 terms of the AP: 10, 6, 2, ... is ______.
An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429. Find the AP.
If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is ______.
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?
Find the middle term of the AP. 95, 86, 77, ........, – 247.
