Question

In an AP of five terms, the sum of the last 4 terms is 38 and the product of
the 2nd and 5th is 70. Find the progression.

Answer 1

Step-by-step explanation:

Let 5 tems are a-2d, a-d, a, a+d, a+2d

according to 1st condition,

a-d+a+a+d+a+2d= 38

4a+2d=38

dividing both sides by 2,

2a+d=19

d=19-2a.... 1

according to 2nd condition,

(a-d) (a+2d) = 70

after solving this the progration is 2,5,8,11,14.

Answer 2

Given:

Sum of last 4 terms is 38.

Product of 2nd and 5th term is 70.

To find: the AP.

Solution:

Let 5 terms are $a-2d, a-d, a, a+d, a+2d$.

Understand that, according to 1st condition,$a-d+a+a+d+a+2d= 38$

 $\[ \Rightarrow 4a + 2d = 38\]$

dividing both sides by 2,

$\[ \Rightarrow 2a + d = 19\]$

$\[ \Rightarrow d = 19 - 2a\]$              -------(1)

And according to 2nd condition,

$\[\left( {a - d} \right) \times \left( {a + 2d} \right) = 70\]$ ------(2)

Solve equations (1) and (2) to find the arithmetic progression.

Hence, the progression is $2,5,8,11,14$respectively.