Question

find 10th term whose fifth term is 24 and difference between 7th term and 10th term is 15​

Answer 1

$a5 = a + 4d = 24 - - - - - (1) \\ a10 - a7d \\ a + 9d -( a + 6d) = 15 \\ 9d - 6d = 15 \\ 3d = 15 \\ d = 5 \\ putting \: value \: of \: d \: in \: (1) \\ a + 4d = 24 \\ = )a + 4 \times 5 = 24 \\ a = 24 - 20 \\ a = 4$

$a10 = a + 9d \\ 4 + 9 \times 5 \\ 4 + 45 \\ 49$

Answer 2

10th term of AP is -1.

Given:

• In an A.P.; Fifth term is 24.
• Difference between 7th term and 10th term is 15.

To find:

• Find the 10th term.

Solution:

Concept/Formula to be used:

General term of AP: $\bf a_n = a + (n - 1)d$

here,

a: first term

d: Common difference

n: number of term

Step 1:

Write equation for 5th term.

$a_5 = 24$

or

$\bf a + 4d = 24...eq1$

Step 2:

Write equation for difference between 7th term and 10th term.

$a_7-a_{10} = 15$

or

$a + 6d - a - 9d = 15$

or

$- 3d = 15$

or

$\bf d = - 5$

Step 3:

Put value of d in eq 1.

$a + 4( - 5) = 24$

or

$a - 20 = 24$

or

$\bf a = 44$

First term is 44.

Step 4:

Find 10th term.

Here

a= 44

d= -5

$a_{10} = 44 + 9( - 5)$

or

$a_{10} = 44 - 45$

or

$\bf \red{a_{10} = - 1}$

Thus,

10th term of AP is -1.

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