Question

The sum of the 5th and the 7th terms of an Arithmetic Progression are 52
and the 10th term is 46. Find the Arithmetic Progression.​

Answer 1

Answer:

1, 6, 11, 16

Step-by-step explanation:

AP:- 1, 6, 11, 16

Answer 2

꧁SOLUTION ꧂

✧♥༻༺♥✧

✼GIVEN✼

• The sum of 5th and 6th term=52
• The 10th term of AP=46

✼FIND:- ARITHMETIC PROGRESSION

✼According to the above information✼

• by using formula of Tn

$↪t5 = a + (n - 1)d \\ ↪a + (5 - 1)d \\ ↪a + 4d$

• similarly

$↪t6 = a + (6 - 1)d \\ ↪a + 5d$

• sum of 5th and 6th term

$↪a + 4d + a + 5d = 52 \\ ↪2a + 9d = 52.....(1)$

• similarly using formula of Tn to find T10

$↪t10 = a + (10 - 1)d = 46 \\ ↪a + 9d = 46.......(2)$

• equation 1 and 2 putting together

$↪2a + 9d = 52 \\ ↪2a + 18d = 92 \\ ↪ - 9d = - 50 \\ ↪d = \frac{50}{9}$

• putting the value of d in 1

$↪2a + 9d = 52 \\ ↪2a + 9 \times \frac{50}{9} = 52 \\ ↪2a + 50 = 52 \\ ↪2a = 52 - 50 \\ ↪a = 1$

➜Hence:-

• the AP are

➜1+50/9=59/9

➜1+59/9=68/9

➜1+68/9=77/9

★ARITHMETIC PROGRESSION

• 59/9 ,68/9 ,77/9-------