Advertisements
Advertisements
प्रश्न
Find the sum of the following arithmetic series:
`7 + 10 1/2 + 14 + ....... + 84`
उत्तर
The given arithmetic series is `7 + 10 1/2 + 14 + ....... + 84`
` Here , a = 7 , d = 10 1/2 - 7 = 21/ 2 - 7 = (21-4)/2 = 7/2 and l = 84.`
Let the given series contains n terms. Then,
an = 84
`⇒ 7 + (n-1) xx 7/2 = 84 [ a_n = a + (n-1) d ]`
` ⇒ 7/2 n + 7/2 = 84`
`⇒ 7/2 n = 84 - 7/2 = 161/2`
`⇒ n = 161/7 = 23`
∴ Required sum`= 23/2 xx (7 + 84) [ s_n = n/2 (a+l) ]`
`=23/2 xx 91`
=`2030/2`
`1046 1/2`
APPEARS IN
संबंधित प्रश्न
Find the term t15 of an A.P. : 4, 9, 14, …………..
Find the sum of the following arithmetic series:
34 + 32 + 30 +...+10
Decide whether the following sequence is an A.P., if so find the 20th term of the progression:
–12, –5, 2, 9, 16, 23, 30, ..............
Find the 27th term of the following A.P.
9, 4, –1, –6, –11,...
Find the 23rd term of the following A.P.: 9, 4,-1,-6,-11.
How many multiples of 4 lie between 10 and 205?
Find t5 if a = 3 आणि d = −3
How many two-digit numbers are divisible by 5?
Activity :- Two-digit numbers divisible by 5 are, 10, 15, 20, ......, 95.
Here, d = 5, therefore this sequence is an A.P.
Here, a = 10, d = 5, tn = 95, n = ?
tn = a + (n − 1) `square`
`square` = 10 + (n – 1) × 5
`square` = (n – 1) × 5
`square` = (n – 1)
Therefore n = `square`
There are `square` two-digit numbers divisible by 5
The nth term of an A.P. 5, 8, 11, 14, ...... is 68. Find n = ?
In an A.P. if the sum of third and seventh term is zero. Find its 5th term.
