For an A.P., it is given that the first term (a) = 5, common difference (d) = 3 and the n∧th term (an) = 50. Find n and sum of first n terms (Sn) of the A.P

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CBSE 10th Class Mathematics

Past year question paper
Year 2020
SET 1, Code Number – 30/5/1
Question Number – 31
Arithmetic progression problem
use the formula of n∧th term

Given, for an AP

a = 5, d = 3, an = 50

n = ? Sn = ?

an = a+(n – 1)d = 50

5 + (n – 1)3 = 50

(n – 1) 3 = 45

n – 1 = 15

n = 16

Sn = n/2 [a + an]

S16 = 16/2 [a + a16]

S16 = 8 [5 + 50]

= 8 × 55

S16 = 440

n = 16