Question

in an arithmetic progression, the first term is -13, the 20th term is 82 and the last term is 112.
a) find the common difference and the number of terms
b) find the sum of the terms in this progression

Answer 1

Answer:

A. Common difference = 5, Last term = 26

B. Sum of all the terms in progression = 1287

Step-by-step explanation:

Data:

First term is -13 (a)

20th term is 82(T 20th)

Last term is 112(T nth)

A. Find the common difference(d) and the number of terms(n)

T 20th = a + 19d

82 = -13 + 19d

82 + 13 = 19d

95/19 = d

d = 5 - Ans

and

T nth = a + (n-1)d        ( We have to find n : the number of terms)

112 = -13 + 5n -5

112 =-18 + 5n

112 + 18 = 5n

130/5 = n

n(number of terms) = 26 - Ans

B. Find the sum of the terms(Sn) in this progression

Sn = n/2 × (first term + last term)

= 26/2 × (-13 + 112)

= 13 × (99)

Sum of the terms in this progression = 1287 - Ans