Question

Find the first term of an arithmetic progression whose 7th and 13th terms are respectively 42 and 78

Answer 1

the first term ofA. P is=24

Answer 2

Answer: The first term is 6.

Step-by-step explanation:

Since we have given that

7th term is 72

So, it becomes,

$a_7=a+6d=42$

13th term is 78

So, it becomes,

$a_{13}=a+12d=78$

So, from both the equations, we get that

$a+6d=42\\\\(a+12d=78)\\\\---------------------------------\\\\-6d=42-78\\\\-6d=-36\\\\d=\dfrac{36}{6}=6$

So, the first term would be

$a+6d=42\\\\a+6\times 6=42\\\\a+36=42\\\\a=42-36\\\\a=6$

Hence, the first term is 6.