Question

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, the common differences.

Answer 1

Answer:

The number of terms is  6 and common difference is 5.

Step-by-step explanation:

Given :  

First term, a = 8, nth term, an (l) = 33 and Sn = 123

By using the formula ,Sum of nth terms , Sn = n/2[a + l]

123 = n/2 [8 + 33]

123 × 2 = n × 41

246 = 41n

n = 246/41

n = 6

Number of terms, n = 6  

By using the formula ,an = a + (n - 1)d

33 = 8 + (6 – 1) d

33 = 8 + 5d

33 – 8 = 5d

25 = 5d

d = 25/5

d = 5

Common Difference ,d = 5  

Hence, the number of terms is  6 and common difference is 5.

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Answer 2

Step-by-step explanation:

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