Advertisements
Advertisements
प्रश्न
In an A.P., if S5 + S7 = 167 and S10=235, then find the A.P., where Sn denotes the sum of its first n terms.
Advertisements
उत्तर
`"S"_5+ "S"_7= 167 and "S"_10=235`
Now `"S"_n=n/2[ 2a + (n-1) d ]`
`"S"_5 + "S"_7=167`
⇒ `5/2 [ 2a + 4d ] + 7/2 [ 2a + 6d ] =167`
⇒ 12a + 31d = 167 .......(i)
also `"S"_10=235`
∴ `10/2 [ 2a + 9d ] = 235`
2a + 9d = 47 .........(ii)
Multiplying equation (2) by 6, we get
12a + 54d = 282 .....(3)
(-) 12a + 31d = 167
- - -
23 d = 115
`therefore d = 5`
Substituting value of d in (2), we have
2a + 9(5) = 47
2a + 45 = 47
2a = 2
a = 1
Thus, the given A.P. is 1, 6, 11, 16 ,..........
APPEARS IN
संबंधित प्रश्न
In an AP given an = 4, d = 2, Sn = −14, find n and a.
If the 10th term of an AP is 52 and 17th term is 20 more than its 13th term, find the AP
Find the common difference of an AP whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.
The fourth term of an A.P. is 11. The sum of the fifth and seventh terms of the A.P. is 34. Find its common difference.
Write an A.P. whose first term is a and common difference is d in the following.
a = –3, d = 0
Find the first term and common difference for the following A.P.:
5, 1, –3, –7, ...
In an A.P. 19th term is 52 and 38th term is 128, find sum of first 56 terms.
The sum of the first three numbers in an Arithmetic Progression is 18. If the product of the first and the third term is 5 times the common difference, find the three numbers.
Find the next 4 terms of the sequence `1/6, 1/4, 1/3`. Also find Sn.
In a ‘Mahila Bachat Gat’, Kavita invested from the first day of month ₹ 20 on first day, ₹ 40 on second day and ₹ 60 on third day. If she saves like this, then what would be her total savings in the month of February 2020?
