Question

the sum of a series of terms in AP is 128 if the first term is 2 and last term is 14 find the common difference

Answer 1

Hey !!!

Given :- Sum of terms in A.P is 128
first term = 2
last term = 14

We know sum formula of A.P = n/2 ( a + l)
where a is first term
n is no . of terms
l is last term .

So on the formule

128 = n/2 (2 + 14)

128 = 8n

n = 128/8

n = 16

But common difference = ?

tn = a + (n- 1) d

14 = 2 + ( 16-1)d


12 = 15d

12/15 = d

4/5 = d

common difference= 4/5 Answer

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Hope it helps you !!!

@Rajukumar111

Answer 2

First term ( a ) = 2

Last term ( L ) = 14

Sum of the terms of an AP = 128

N/2 × ( First term + Last term ) = 128

N/2 × ( 2 + 14 ) = 128

N/2 × 16 = 128

8N = 128

N = 16 .

Number of terms = 16.

Last term ( L ) = 14

a + ( n - 1 ) × d = 14

2 + ( 16 - 1 ) × d = 14

2 + 15d = 14

15d = 12

d = 4/5.


Hence,

common difference ( D ) = 4/5.