Question

An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term??​

Answer 1

${\huge{\boxed{\underline{\bf{\color{orchid}{Required \: \: Answer}}}}}}$

To Solve:

• Find 29th Term.

Given:

• AP has 50 terms.
• 3rd Term - 12
• Last Term ( 50th ) - 106

Solⁿ:

3rd Term can be written as:

a + 2d = 12 -----------(1)

Last Term (50th) can be written as:

a + 49d = 106 -----------(2)

Now, Solving Through Elimination Method:

ㅤㅤㅤaㅤ+ㅤ49dㅤ= +106

ㅤㅤ ±aㅤ±ㅤ 2dㅤ= ±12

ㅤㅤ￣￣￣￣￣￣￣￣￣￣

ㅤㅤㅤㅤㅤ47d = 94

ㅤㅤㅤㅤㅤd = 2

» Value Of a :-

= a + 2d = 12

= a + 2(2) = 12

= a + 4 = 12

= a = 12 -4

= a = 8

• 29 th Term

${a}^{29} = a + (n - 1)d \\ \\ {a}^{29} = 8 + (29 - 1)2 \\ \\ {a}^{29} = 8 + 28 \times 2 \\ \\ {a}^{29} = 8 + 56 \\ \\ { \boxed{ \color{darkblue}{a}^{29}= 64}}$

HOPE IT HELPS

MARK BRAINLIEST PLS :)