Advertisements
Advertisements
प्रश्न
In an A.P. (with usual notations) : given a = 8, an = 62, Sn = 210, find n and d
Advertisements
उत्तर
a = 8, an = 62, Sn = 210
an = a + (n – 1)d
62 = 8 + (n – 1)d
(n – 1)d = 62 – 8 = 54 ...(i)
Sn = `n/(2)[2a + (n - 1)d]`
210 = `n/(2)[2 xx 8 + 54]` ...[From (i)]
420 = n(16 + 54)
⇒ 420 = 70n
n = `(420)/(70)` = 6
∴ (6 – 1)d = 54
⇒ 5d = 54
⇒ d = `(54)/(5)`
Hence d = `(54)/(5) and n = 6`.
APPEARS IN
संबंधित प्रश्न
The sum of three numbers in AP is 3 and their product is –35. Find the numbers.
The first term of an AP is p and its common difference is q. Find its 10th term.
Sum of 1 to n natural numbers is 36, then find the value of n.
If first term of an A.P. is a, second term is b and last term is c, then show that sum of all terms is \[\frac{\left( a + c \right) \left( b + c - 2a \right)}{2\left( b - a \right)}\].
The sum of first n terms of an A.P is 5n2 + 3n. If its mth term is 168, find the value of m. Also, find the 20th term of this A.P.
There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.
Write the common difference of an A.P. whose nth term is an = 3n + 7.
Q.13
A merchant borrows ₹ 1000 and agrees to repay its interest ₹ 140 with principal in 12 monthly instalments. Each instalment being less than the preceding one by ₹ 10. Find the amount of the first instalment.
The sum of A.P. 4, 7, 10, 13, ........ upto 20 terms is ______.
