4.In an A.P The first term is 8, nth term is 33 and the sum to
first n terms is 123. Find n and d?
Answers
GIVEN:
First term of an AP = a = 8
nth term of an AP = an = 33
Sum of first 'n' terms of AP = Sn = 123
TO FIND:
n and common difference
SOLUTION:
We know that,
Sn = n/2 [ a + an ]
= n/2 [ 8 + 33 ]
= n/2 [ 41 ]
=> 123= 41n/2
=> 123 × 2 = 41n
=> 246 = 41n
=> n = 246/41
=> n = 6
=> Thus n = 6
Now,
an = a + (n - 1)d
= 8 + (6 - 1)d
= 8 + (5)d
=> 33 = 8 + 5d
=> 5d = 33 - 8
=> 5d = 25
=> d = 25/5
=> d = 5
Common Difference = 5
Therefore, n = 6 and d = 5
Answer:
Given:
In an A.P The first term is 8, nth term is 33 and the sum to first n terms is 123.
Find:
Find 'n' and 'd' ?
According to question:
⇒(a) = 8
⇒ (aₙ) = 33
⇒ (sₙ) = 123
Well, equation (1) taking (aₙ) = 33:
⇒ a + (n - 1) d = 33
⇒ (n - 1) d = 33 - 8
⇒ (n - 1) d = 25 – Equation (1)
Equation (2) taking (sₙ) = 123:
⇒ n/2 (a + an) = 123
⇒ n/2 (8 + 33) = 123
⇒ n/2 (n/2 × 41) = 123
⇒ n = 123 × 2/41 [Cancelling]
⇒ n = 6 – Equation (2)
Adding suitable values to Equation (2) in Equation (1):
⇒ (n - 1) d = 25
⇒ (6 - 1) d = 25
⇒ d = 5
Therefore, n = 6 and d = 5.