Question

The first term,seventh term and nth term of an AP are 4, 28 and 32 respectively. Calculate the number of terms in the sequence.

Answer 1

$a_n=a_1+(n-1)d.$

$a_1=4.$

$a_7=a_1+(7-1)d\to 28=4+6d\to d=4.$

$a_n=4+4(n-1) \to 32=4+4(n-1) \to n=8.$

There are 8 terms in the sequence.